For the Direct free kick, the game restarted.
What does a soccer direct free kick entail?There are two different kinds of free kicks used in soccer: direct and indirect.The term "direct free kick" refers to a kick that can be used as a direct strike.Indirect free kicks require a second touch before the ball can be used as a shot at goal.
A direct penalty kick is what?If a player attacks an opponent in a way that the referee deems to be irresponsible, reckless, or employing excessive force, the referee will award a direct free kick.jumps, kicks, or makes an attempt to kick.
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A proton moves at 3.80 105 m/s in the horizontal direction. It enters a uniform vertical electric field with a magnitude of 9.20 103 N/C. Ignore any gravitational effects. (a) Find the time interval required for the proton to travel 4.50 cm horizontally. 118.42 Correct: Your answer is correct. ns (b) Find its vertical displacement during the time interval in which it travels 4.50 cm horizontally. (Indicate direction with the sign of your answer.) mm (c) Find the horizontal and vertical components of its velocity after it has traveled 4.50 cm horizontally.
Answer:
(a) The time interval required for the proton to travel 4.50 cm horizontally is
t = (4.50 cm) / (3.80 x 105 m/s) = 118.42 ns
(b) The vertical displacement of the proton during the time interval is
dY = (F × t2) / 2m = (9.20 x 103 N/C × (118.42 ns)2) / (2 × 1.67 x 10-27 kg) = 0.0033 mm
(c) The horizontal and vertical components of the velocity after the proton has traveled 4.50 cm horizontally are
Vx = 3.80 x 105 m/s
Vy = (F × t) / m = (9.20 x 103 N/C × 118.42 ns) / (1.67 x 10-27 kg) = 1.90 x 105 m/s
25. What force must be exerted on the pedal cylinder of a hydraulic lift to support the weight of a 2000-kg car (a large car) resting on the wheel cylinder
A hydraulic lift's master cylinder must be subjected to a force of 136N.
What is the tenet of the Archimedes Principle?According to Archimedes' principle, an object that is totally or partially submerged in a fluid will feel upward buoyant force that is equivalent in strength toward the point of gravity here on displaced fluid.
Where is the principle of Archimedes used?The design principle for vessels and submarines uses Archimedes' principle. The Archimedes principle is the foundation of hydrometers.
According to Archimedes' principle:
F1 / A1 = F2 / A2
F2 = (A2 / A1) * F1
Also, the formula for the force is F = mg.
The formula for the area of the cylinder is A = , therefore we get
F2 = ( π [tex](r2)^{2}[/tex] / π [tex](r1)^{2}[/tex] ) * mg
Since the cylinders' diameter is 2 cm and 24 cm, r1 = 12 and r2 = 1.
Substituting the values to the derived equation, we get
F2 = ( π [tex](1)^{2}[/tex] / π [tex](12)^{2}[/tex] ) * 2000 * 9.8
2 = 136 N
Thus, the force exerted must be 136N.
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How do you calculate the speed of an object rolling down a ramp?
We can calculate the speed of an object rolling motion a ramp by using the equation of motion in which we consider rolling and a tangential force acting on it.
Rolling motion occurs when an object rolls down over a height from the ramp or from any other sloppy or rough surface. the surface can be both smooth or rough, depending on it the friction acts on the object that is rolling over the ramp. we also consider the rolling tangential force in our calculation along with other forces when we tend to calculate the rest of the things. We can calculate the speed of an object rolling motion a ramp by using the equation of motion in which we consider rolling and a tangential force acting on it. Hence by this we can consider that we can calculate the rolling of any object by the equation of motion.
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A student wants to investigate the motion of a ball by conducting two different experiments, as shown in Figure 1 and Figure 2 above. In Experiment 1, the student releases a ball from rest and uses a slow-motion camera to film the ball as it falls to the ground. Using video analysis, the student is able to plot the ball’s horizontal position x and vertical position y as a function of time t. In Experiment 2, the student horizontally rolls the same ball off a table, and uses video analysis to plot the ball’s horizontal position x and vertical position y as a function of time t starting from the instant the ball leaves the table. The graphs from each experiment are shown above along with each graph’s best-fit curve line.
Question:
Suppose that Experiment 1 and Experiment 2 are conducted at the same time; one student drops the ball from rest at the same instant that a second student horizontally rolls an identical off the table. After both balls have traveled half their vertical distance to the floor, what is the acceleration of the center of mass of the two-ball system relative to Earth?
A) Equal to g
B) Less than g, but not zero
C) Less than g , but not zero
D) Zero
The acceleration of the center of mass of the two-ball system relative to Earth is equal to g after the balls have travelled for half their vertical distance to the ground, option A.
What is the center of mass of any object?The total force acting on the system is equal to the acceleration of the center of mass multiplied by the total mass of the system. When applied to an extended object, Newton's second law, F = ma, predicts the motion of a specific reference point for this object. The center of mass is the name given to this reference point.
When we throw an object upward, gravity acts on it, and the acceleration it experiences is the inverse of the acceleration caused by gravity, i.e. deceleration. As a result, the acceleration of each ball will be g. As a result, the acceleration of the center of mass of the two balls thrown upward is g.
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A picture frame hung against a wall is suspended by two wires attached to its upper corners. If the two wires make the same angle with vertical, what must this angle be if the tension in each wire is equal to 0.75 of the weight of the frame?
(Neglect any friction betweem the wall and the picture fame)
The angle must be formed if the tension in each cable is equal to 0.75 of the frame weight is 83.6⁰.
By using the parallelogram law of vector addition, it is possible to calculate the angle between the two wires.
a² + b² - 2abcosθ = R²
Where;
R = is the outcome vector = the frame's weight ⇒ W
Angle between the two wires equals 0.75W for the first wire's tension and 0.75W for the second wire's tension.
(0.75W)² + (0.75W)² - 2(0.75W x 0.75W) cosθ = W²
1.125W² - 1.125W² cosθ = W²
= 1.125W²(1 - cosθ)
W²/1.125W² = 1 - cosθ
0.8889 = 1 - cosθ
cosθ = 1 - 0.8889
cos θ = 0.1111
θ = arc cos(0.1111)
θ = 83.6⁰
So, the angle must be formed if the tension in each cable is equal to 0.75 of the frame weight is 83.6⁰
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It is known that a damped oscillator has a maximum displacment that is 13.5% of the original amplitude after 0.60 s. What is the value of the time constant
The value of the time constant is = 0.2996 s. Due to the fluid's dampening effect, the oscillations' amplitudes reduce. ma=−bv−kx.
How long does it take for the damped oscillations' amplitude to decrease to half of what it was initially?Its amplitude decreases by half after every ten oscillations. Find the starting time at which the amplitude becomes 11000 times as large as it was initially: Q. A damped harmonic oscillator's displacement is determined by the equation x(t)=e01.
How do amplitude and oscillation relate to one another?In an oscillating system, the amplitude is the amount by which the oscillating variable changes with each oscillation. For instance, sound waves in the air oscillate the atmospheric pressure, and the amplitude of each oscillation is proportional to the variation in the pressure.
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Can nuclei of the same element have different values of Z? Of N? Of A?
Check all that apply.
O 1 Nuclei of the same element must have the same values of Z, N, and A.
O 2 Nuclei of the same element can have different values of Z.3
O 3 Nuclei of the same element can have different values of A.
O 4 Nuclei of the same element can have different values of N.
Nuclei of the same element can have different values of Z, N, and A, as these values are all related to the number of protons, neutrons, and nucleons in the nucleus, respectively. Therefore, option 2, 3, and 4 are correct.
Nuclei of the same element can have different values of Z, N, and A due to the number of protons, neutrons, and nucleons they contain, respectively. This is because the number of these particles in the nucleus can vary, although they all will still be the same element. Therefore, option 2, 3, and 4 are correct and option 1 is incorrect.
Nuclei of the same element can have different values of Z, N, and A, as these values are all related to the number of protons, neutrons, and nucleons in the nucleus, respectively. Therefore, option 2, 3, and 4 are correct.
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What is the speed of a truck that travels 10 km in 20 minutes?
Answer:
8.3 m/s
Explanation:
Here's the answer in m/s:
(10 km)(1000 m/km) = 10000 m
(20 min)(60 s/min) = 1200 s
speed = d/t = 10000m / 1200s = 8.3 m/s
If a container is stressed beyond its limits of recovery and opens up, then it is in this event of the General Hazardous Materials Behavior Model.
A container is said to have breached when it has been overstressed beyond its point of recovery.
The GEBMO model enables a systematic evaluation of the outcomes that are most likely to occur when a hazardous material container is strained. Hazardous material containers typically have the capacity to hold that material under typical shipping, storage, and use circumstances. Thus, API gravity is a measure of the density of a petroleum liquid in relation to water (also known as specific gravity). It is used to compare petroleum liquid densities. For instance, if one petroleum liquid has a higher API gravity than another because it is less dense.Specific gravity (Sp.Gr. or SG) is the weight or density of a liquid or solid relative to water. Floaters and sinkers have specific gravities below that of water and are very immiscible with itTo know more about Hazard here
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The____of a conductor is defined as the diameter of the conductor in mils, squared.
The cross-sectional area of a conductor is defined as the diameter of the conductor in mils, squared.
What is conductor?
A conductor is a material or object that allows the flow of electric current. It is a material that has a large number of free electrons which can move freely between atoms, allowing for the current to flow through the material. Conductors can be either solid or liquid, and can be used to create electrical circuits and systems. Common conductors used in electrical systems include copper, aluminum, silver, and gold. These materials have high electrical conductivity, meaning they have low resistance and allow for large amounts of electric current to pass through them. Conductors are essential in many electronics and electrical devices, as they are responsible for carrying the electric current from one component to another.
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It took the bike messenger 36 minutes to ride from the school to the blue house. If they are 2160 meters apart, what was the messenger's velocity
The bike messenger's velocity will be 1 m/s.
Given as per the question is,
Distance between school and the blue house is 2160 meters
Time taken by the bike messenger is 36 minutes
Velocity is to be calculated.
Converting minutes into seconds,
36 minutes = 36 X 60 = 2160 seconds.
Velocity of an object can be calculated by the formula as,
Velocity = Distance/ Time
Substituting the values as per the formula above,
Velocity = 2160/2160 = 1 m/s
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You and your friend, who weighs the same as you want to go to the top of the Eiffel Tower Your friend takes the elevator straight up. You decide to walk up the spiral stairway, taking longer to do so. Compare the gravitational potential energy of you and your friend, after you both reach the top. Your gravitational potential energy is greater than that of your friend, because you traveled a greater distance in getting to the top. Your friend's gravitational potential energy is greater than yours, because he got to the top faster Both of you have the same amount of gravitational potential energy at the top. Dit is impossible to tell, since the times you both took are unknown Impossible to tell since the distances you both traveled are unknown
You and your friend will have the same potential energy at the top of the tower because gravitational potential only depends on height and not on how an object got there.
What does potential energy mean?The power that a substance retains as a result of its position in relation to other things, internal pressures, electric charge, or other substances is known as potential energy in physics. Potential energy is a form of energy that is stored but is dependent on the interactions of different system components.
A steel ball has more potential energy if it is raised above the ground as opposed to dropping to it. The energy that is present in everything that is raised from rest and has the potential to be released at a later time is known as potential energy.
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An object that is moving in a circle at a constant speed has a velocity vector that is directed ________and an acceleration vector that is directed ________.
A directed velocity vector and a directed velocity acceleration vector characterise an item travelling in a circle at a constant speed.
When an item is travelling in a circle at a constant speed, what is its acceleration?Consequently, an object travelling in a circle at constant speed is speeding up its approach to the circle's centre. Centripetal acceleration is the term used to describe the speed toward the centre of the circle.
What happens to an object's velocity when it rotates in a circle at a constant speed?There is a fluctuating velocity for an object in a circular orbit travelling at a constant speed. Considering that velocity is a vector quantity that depends on both speed and direction, this makes sense. Accelerating is the object in orbit.
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How do you find thermal energy from kinetic and potential energy?
Thermal energy can be found from kinetic and potential energy by calculating the amount of work done on an object. Work is equal to the amount of force multiplied by the distance moved by the object.
The Kinetic energy is equal to the mass of the object multiplied by the square of its velocity. Potential energy is equal to the mass of the object multiplied by the acceleration of gravity multiplied by the height of the object. Thermal energy is equal to the sum of the kinetic and potential energies.
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Justin throws a 10. 0-g ball straight
down from a height of 2. 0 m. The ball
strikes the floor at a speed of 7. 5m/s.
What was the initial speed of the ball?
The ball's initial speed as it descended straight down from a height was 17.5 miles per hour.
The starting velocity is the speed at time t = 0. (u). It is the speed at which motion first becomes apparent. Four equations can be used to calculate initial velocity: (1) If time, acceleration, and end velocity are known, the initial velocity can be calculated using the formula u = v - at.
Calculation:We can simply use the following equation of motion to solve this:v² - u² = 2 × a × s
here, v = final velocity = 7.5 m/s
a = 9.81 m/s^2
s = 2.0 m
Solving for u (initial velocity) we get:
(7.5)² - u² = 2 × 9.8 × 2
56.25 - u² = 39.2
u² = 56.25 - 39.2
u² = 17.05
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How do you calculate lever arm in torque?
We can find the torque of lever arm by the formula Torque(T)=Force * perpendicular distance.
A torque is an action that causes objects to rotate. A torque is required to rotate an object, just as a force is required to move an object in a line. Torque is created by force, but it also depends on where the force is applied and the point about which the object rotates.
Force and lever arm are not always perpendicular. When the force and lever arm are not perpendicular, trigonometry is required to calculate the length of the lever arm. The force applied is perpendicular to the surface of the object rotating. When this force is at an angle θ with the plane of the object, the perpendicular force requires the use of the sine function.
When an object is in rotational equilibrium, the net torque applied to it is zero. For example, if an object such as a see-saw is not rotating, you know the torque on each side is balanced Rotational equilibrium is often used to determine unknown forces. Any object that is not moving is in rotational equilibrium and in translational equilibrium.
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A box is released from the top of a frictionless track. It starts from rest and has a speed of 14 m/s at the bottom. What is the height of the track
If we use the aceleration equation, we can calculate the height value: The height of the track is: 98.04 m,
The height of the track can be calculated using the equation:
h = (v^2)/(2g)
Where h is the height, v is the velocity, and g is the acceleration due to gravity (9.8 m/s^2).
Therefore, the height of the track is:
h = (14^2)/(2*9.8) = 98.04 m
The equation h = (v^2)/(2g) is derived from the equation of motion for an object moving in a uniform gravitational field. This equation states that the change in potential energy is equal to the kinetic energy of an object. The potential energy of an object is determined by its height in the gravitational field, and the kinetic energy of an object is determined by its velocity. Therefore, the equation of motion can be used to calculate the height of an object, given its velocity.
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You're in the back of a friend's pickup truck when it stalls on a hill. You jump out, get behind the truck and push with all your might (300 N) in a vain attempt to keep the truck from accelerating down the hill. The force the truck exerts on you is: less than 300 N 300 N greater than 300 N
The force the truck exerts on you is 300 N.
What is meant by force?
A force in physics is an effect that has the power to alter an object's motion.Intuitively, a push or a pull can also be used to describe force.Being a vector quantity, a force has both magnitude and direction. The SI unit of newton is used to measure it (N). The letter F stands for force (formerly P).According to Newton's second law's original formulation, an object's net force is equal to the speed at which its momentum is changing over time. According to this law, an object's acceleration is inversely proportional to the net force acting on it, is in the direction of the net force, and is directly proportional to the mass of the object if its mass is constant.To learn more about force refer to
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how long after closing the switch s will the potential across each capacitor be reduced to 15.0 v ?
The time taken can be calculated by the equation: t = -RC ln(15/50)
To determine how long after closing the switch s the potential across each capacitor will be reduced to 15.0 V, we need to know the initial potential across the capacitors, the capacitance value and the resistance in the circuit.
When a switch is closed, the potential across a capacitor decreases exponentially with time according to the equation:
V(t) = V0e^(-t/RC)
Where V0 is the initial potential across the capacitor, t is time, R is the resistance in the circuit, and C is the capacitance.
In this case, the initial potential across each capacitor is 50.0 V, and the resistance in the circuit is 80 ohms.
To find the capacitance value we need to know that the capacitors are parallely connected, which means that the total capacitance is the sum of the individual capacitances:
Ctotal = C1 + C2
Once we have the capacitance value, we can find the time constant RC:
RC = R / Ctotal
Now we can use the equation above to find the time it takes for the potential to decay to a certain percentage of the initial value.
For example, if we want to find the time it takes for the potential to decay to 15.0 V (30% of the initial value), we can use the following equation:
15.0 V = 50.0 Ve^(-t/RC)
and we can solve for t:
t = -RC ln(15/50)
It's worth noting that this is an estimation and that in real world situations the resistance and capacitance values are also affected by other factors such as leakage current or parasitic capacitances.
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Three loops of wire move near a long straight wire carrying a current as in the following figure. (a) What is the direction of the induced current, if any, in loop A? O clockwise O counterclockwise
O No current is induced. (b) What is the direction of the induced current, if any, in loop B? O clockwise O counterclockwise O No current is induced. (c) What is the direction of the induced current, if any, in loop C? O clockwise O counterclockwise O No current is induced.
(A) The current in the long straight wire produces a magnetic field that is perpendicular to its direction of flow.
What is Counter clockwise ?
Counter clockwise is a direction opposite to the usual clockwise direction. It is often used to describe the direction of rotation or movement, such as the turning of a wheel, the orbits of planets, or the hands of a clock. Counterclockwise motion can also be referred to as "widdershins" or "anticlockwise."
This magnetic field interacts with the loops of wire, inducing a current in them. The direction of the current in loop A is clockwise due to the right hand rule.
(B) No current is induced. Since the flux through loop B is not changing, no induced current is created.
(C) No current is induced. Since loop C is not moving, the changing magnetic field will not induce any current in it.
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Complete Questions:
(a) What is the direction of the induced current, if any, in loop A?
A) clockwise
B) counterclockwise
C) No current is induced.
(b) What is the direction of the induced current, if any, in loop B?
A clockwise
B counterclockwise
C No current is induced.
(c) What is the direction of the induced current, if any, in loop C?
A clockwise
B counterclockwise
C No current is induced.
How does dynamic stretching help an individual prepare for an activity brainly?
Dynamic stretching helps to prepare the body for an activity by increasing:
body temperatureimproving range of motionactivating the muscles and nervous system for the activity. also helps to reduce the risk of injury by improving the body's ability to move through a full range of motion.improving coordination and balance.What is dynamic stretching?Dynamic stretching is a form of stretching that involves active, controlled movements such as swinging, bouncing, and twisting. The goal of dynamic stretching is to improve range of motion and flexibility while preparing the body for physical activity.
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A crate of eggs is located in the middle of a pickup truck as the truck rounds a corner in the road. The curve has a radius of 35 m. If the coefficient of static friction between the crate and the truck is 0.600, how fast can the truck move without the crate sliding
The speed of the truck is 14.3m/s without the crate sliding.
What is the equation for static friction?The resistive friction force (Fr) multiplied by the usual or horizontal pressure (N) pushing the things together yields the frictional coefficient (fr), which is a numerical value. The formula fr = Fr/N serves as a representation of it.
Calculation -:Call the mass of the egg crate m. The forces on it are its weight Fg =mg vertically down, the normal force n of the truck bed vertically up, and static friction (fs) directed to oppose relative sliding motion of the crate on the truck bed. The friction force is directed radially inward. It is the only horizontal force on the crate, so it must provide the centripetal acceleration. When the truck has maximum speed, friction fs will have its maximum value with fs=μn.
Newton’s second law in component form becomes
∑Fy=ma(y) giving n−mg = 0 or n = mg
∑F(x)=ma(x) giving f(s)= ma(r)
From these equations
μ(s)n ≤ mv²/r and μ(s)mg ≤ mv²/r
The mass divides out. The maximum speed is then
v≤[tex]\sqrt{}[/tex]μrg =[tex]\sqrt{}[/tex]0.600(35.0m)(9.80 m/s²) = v ≤1 4.3m/s.
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Mess Me and You will have nonsense Explain how this riddle relates to mutation in DNA
Nonsense mutations are those point mutations in the DNA where stop codons will appear before the time they should appear.
What are nonsense mutations?At the time of transcribing from DNA to RNA, the template needs to have both start and stop codons for the transcription to occur correctly, but sometimes mutations can occur that do not allow the protein to be produced correctly. This mutation can be permanent which causes damage to the formation of proteins.Sometimes mutations can be beneficial, allowing evolution and helping organisms to be better formed for a new environment.
It is the type of mutation in which a termination codon occurs before the time it should be, instead of giving a codon with a certain amino acid. Which gives a much shorter protein than it should be, giving a non-functional protein.
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N a circuit, when the two conductors leading from the power source touch metal-to-metal, this is called a _____ circuit
In a circuit, when the two conductors leading from the power source touch metal-to-metal, this is called a short circuit
Types of short circuitThere are two types of short circuits, short-to-power and short-to-ground, where electricity takes an unintentional shortcut without going through the intended sensor or actuator.
Short to ground - When there is a short to ground, it refers to the current flowing from the circuit to the car body. Wires can tear and strip their insulation, contacting the body or engine. A short path to ground can result in blown fuses, malfunctioning lights or motors, or “missing” sensors. For example, a scuffed wire might be short to ground, which could cause the headlight fuse to blow, protecting the circuit from overheating, but killing the headlights. Short power - In a wire harness, with many circuits in close proximity, there is a possibility of a short power fault. In this case, wires that are wound or cut can interconnect with each other, allowing current to flow where it is not intended. For example, someone installing an aftermarket device might push a screw through a wire harness, accidentally puncturing and "connecting" some of the wires. Turning on the headlights might send current into the horn, or hitting the brakes might illuminate the taillights.Learn more about short circuit at https://brainly.com/question/18207608.
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An engine with a power output of 110 hp has a thermal efficiency of 28%. Determine the rate of fuel consumption (in kg/hr) if heating valve of the fuel is 44,200kj/kg
The rate of fuel consumption is 6.69 kg/hr.
Solution:
To determine the rate of fuel consumption, we need to calculate the amount of energy required by the engine and divide that by the thermal efficiency.
From the question:
W = 110 hp
η = 28%.
r = ?
First, we can convert the power output from horsepower to watts:
1hp = 746 W
power output = 110 hp x 746 W/hp
= 82016 W
Then, we can calculate the energy required by the engine by multiplying the power output by the time the engine is running:
Energy = Power x time
Without knowing the time the engine runs, we cannot calculate the energy required.
We can calculate the fuel consumption by using the heating value of the fuel and the thermal efficiency.
Fuel consumption = ( Power )
(heating value * thermal efficiency))
So in this case:
Fuel consumption = (82016)
(44200*0.28)
= (82016)
12276
Fuel consumption = 6.69 kg/hr
Hence, the rate of fuel consumption is 6.69 kg/hr.
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Running at 2. 0 m/s, Burce, the 45. 0 kg quarterback, collides with Max, the 90. 0 kg tackle, who is traveling at 7. 0 m/s in the other direction. Upon collision, Max continues to travel forward at 1. 0 m/s.
What is the new velocity of Bruce?(list unknown variable and known variables, write an equation, plug in numbers, and get answer with unit. )
Burce, a 45-kg quarterback, collides with Max, a 90-kg tackle, who is moving at 7.0 m/s in the opposite direction, as he runs at 2.0 m/s. This results in Bruce's new speed being 14 m/s.
Max hits the ground moving forward at a speed of 1.0 m/s. A moving object's velocity is a function of time and measures how quickly its position changes in relation to a frame of reference. When an object is moving, its speed and direction are specified by its velocity. A collision in physics is referred to as an elastic collision when the combined kinetic energy of the two bodies stays constant. A collision that is ideal and absolutely elastic
V1 = (720 - (90)(1))/45
V1 = 14m/s
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define visible light radiation
The upper and lower fixed points of a mercury thermometer corresponds to 9.00mV and 16.50mV on the thermocouple thermometer. The temperature of a warm iron giving a reading of 11.21mV to the nearest whole number is.
To find the temperature of the warm iron, we first need to convert the reading on the thermocouple thermometer to a temperature value. To do this, we will use the formula:
Temperature = (Reading - Lower Fixed Point) / (Upper Fixed Point - Lower Fixed Point) * (Upper Temperature - Lower Temperature) + Lower Temperature
In this case, the lower fixed point is 9.00mV and the upper fixed point is 16.50mV. We also know that the lower temperature is 0°C (the freezing point of water) and the upper temperature is 100°C (the boiling point of water). So, we can plug in these values:
Temperature = (11.21mV - 9.00mV) / (16.50mV - 9.00mV) * (100°C - 0°C) + 0°C
Simplifying, we get:
Temperature = (2.21mV / 7.50mV) * 100°C
And further simplifying, we get:
Temperature = 0.2907 x 100°C
So, the temperature of the warm iron is approximately 29.07°C to the nearest whole number.
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At t = 0, a wheel rotating about a fixed axis at a constant angular acceleration of -0.40 rad/s2 has an angular velocity of 1.5 rad/s and an angular position of 2.3 rad. what is the angular position of the wheel at t = 2.0 s?
At t = 0, the wheel has an angular position of 2.3 rad and an angular velocity of 1.5 rad/s.
Since the wheel is rotating about a fixed axis at a constant angular acceleration of -0.40 rad/s2, we can use the equation for angular position to calculate the wheel's angular position at t = 2.0 s.
Angular position = initial angular position + (initial angular velocity × time) + (1/2 ×angular acceleration ×time²)
Angular position at t = 2.0 s = 2.3 rad + (1.5 rad/s × 2.0 s) + (1/2 ×-0.40 rad/s2 × (2.0 s)²)
Angular position at t = 2.0 s = 2.3 rad + 3.0 rad + -1.6 rad
Angular position at t = 2.0 s = 3.7 rad
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draw the standing wave if the tension is quadrupled while the frequency is held constant
The diagram for the standing wave after the tension is quadrupled while the frequency is held constant has been attached and explained below.
We already know that the frequency of a standing wave is given by,
= f = nv/2l
and
= v = [tex]\sqrt{\frac{T}{m} }[/tex]
In the given problem, the frequency of the wave after the tension is quadrupled will be -
= f2 = 2v/2l
= f2 = v/l
= f2 = 1/l [tex]\sqrt{\frac{T}{m} }[/tex]
Now, since we have quadrupled the tension, we have -
= f = 1/l [tex]\sqrt{\frac{4T}{m} }[/tex]
= f = 2(f2)
So, now we know that the final frequency will be of this form(the image has been attached here) and it would look like this if the tension is quadrupled while the frequency is held constant.
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