The ball has 2.0 Joules of kinetic energy after hitting the wall.
The energy that is moving or doing work is known as an object's kinetic energy. It can be stated using the following formula:
K.E = [tex]\frac{1}{2} mv^2[/tex]
where m is the ball's mass and v is its final velocity following impact.
The rubber ball has a mass of 1.0 kg.
Before the collision, the rubber ball was moving at a speed of 2.0 m/s.
After the collision, the rubber ball's final speed was 2.0 m/s slower.
Following the contact and after it bounces off the wall, the ball's kinetic energy is calculated as follows
K.E = [tex]\frac{1}{2} mv^2[/tex]
K.E = [tex]\frac{1}{2} \times 1 \times (2)^2[/tex]
K.E = 4/2
K.E =2.0 Joules
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The kinetic energy of the ball after it bounces off the wall is 2.0 Joules.
The kinetic energy of an object is the energy that is in motion or performing work. It can be expressed by using the formula:
[tex]K.E=\frac{1}{2} mv^2[/tex]
The mass of the object(rubber ball) = 1.0 kgThe initial speed of the rubber ball before the collision = 4.0 m/sThe final speed of the rubber ball after the collision = - 2.0 m/sThe Kinetic energy of the ball after the collision and when it bounces off the wall is computed as:
[tex]K.E. =\frac{1}{2} *1.0*(2.0)^2[/tex]
K.E. = 2.0 Joules
In physics, the kinetic strength of an item is the energy that it possesses because of its motion. it's far described as the work needed to boost up a frame of a given mass from rest to its said speed. Having gained this power during its acceleration, the frame continues this kinetic power except for its pace adjustments. An equal quantity of labor is carried out by means of the body when decelerating from its current speed to a country of relaxation. officially, kinetic power is any time period in a gadget's Lagrangian which incorporates a spinoff with respect to time.
Kinetic electricity is the power an object has due to its motion. If we need to boost up an item, then we must observe a force. applying pressure calls for us to do paintings. After paintings have been done, strength has been transferred to the item, and the object may be moving with a brand new constant speed.
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Animals conduct_______.
A. cellular respiration
B. photosynthesis
C. both cellular respiration and photosynthesis
20. For each improvement in glider design, engineers follow
O A. the written instructions that are provided in the hang glider build kit.
O B. an iterative process of testing, modifying, retesting, and modifying again.
O C. a complicated process of checks and balances while obtaining financing.
O D. a mathematical process, rejecting designs that don't follow blueprint dimensions.
Turn In
In a physics lab experiment for the determination of moment of inertia, a team weighs an object and finds a mass of 2.15 kg. They then hang the object on a pivot located 0.163 m from the object's center of mass and set it swinging at a small amplitude. As two of the team members carefully count 113 cycles of oscillation, the third member measures a duration of 241 s. What is the moment of inertia of the object with respect to its center of mass about an axis parallel to the pivot axis
Answer:
0.339 kgm²
Explanation:
We know the period of this pendulum, T = 2π√(I/mgh) where I = moment of inertia of the object about the pivot axis, m = mass of object = 2.15 kg, g = acceleration due to gravity = 9.8 m/s² and h = distance of center of mass of object from pivot point = 0.163 m.
Since T = 2π√(I/mgh), making I subject of the formula, we have
I = mghT²/4π²
Now since it takes 241 s to complete 113 cycles, then it takes 241 s/113 cycles to complete one cycle.
So, T = 241 s/113 = 2.133 s
So, Substituting the values of the variables into I, we have
I = mghT²/4π²
I = 2.15 kg × 9.8 m/s² × 0.163 m × (2.133 s)²/4π²
I = 15.63/4π² kgm²
I = 0.396 kgm²
Now from the parallel axis theorem, I = I' + mh² where I' = moment of inertia of object with respect to its center of mass about an axis parallel to the pivot axis
I' = I - mh²
I' = 0.396 kgm² - 2.15 kg × (0.163 m)²
I' = 0.396 kgm² - 0.057 kgm²
I' = 0.339 kgm²
when material allow to heat to pass though them rapidly they are known as __________
Answer:
They are conductors/conductive. Materials that can transfer thermal energy well are conductive.
Explanation:
Answer:when material allow to heat to pass though them rapidly they are known as Conductors
What are conductors
In physics /electrical engineering They allow the flow of charge (electrical current) in one or more directions. Materials made of metal are common electrical conductors.
What are examples of conductors
.Silver
.copper
.iron
.aluminum
.brass
Difference between conductors and insulators?
Insulators a material that is a poor conductor (as of electricity or heat)Whereas Conductors are fantastic at allowing the flow of the heat.
Hope this helps
-Tobie
A diet is to contain at least 2400 mg vitamin C, 1800mg Calcium, and 1200 calories every day. Two foods, a dairy-based meal and a vegan option are to fulfill these requirements. Each ounce of the dairy-based meal provides 50 mg vitamin C, 30 mg Calcium, and 10 calories. Each ounce of the vegan option provides 20 mg vitamin C, 20 mg Calcium, and 40 calories. If the dairy-based meal costs $0.042 per ounce and the vegan option costs $0.208 per ounce, how many ounces of each food should be purchased to minimize costs? What is that minimum cost (per day)?
Answer:
The answer is below
Explanation:
Let x represent the number of ounce of dairy based meal and let y represent the number of vegan option in ounce.
Since the diet must contain at least 2400 mg vitamin C, therefore:
50x + 20y ≥ 2400
Since the diet must contain at least 1800 mg Calcium, therefore:
30x + 20y ≥ 1200
Since the diet must contain at least 1200 calories, therefore:
10x + 40y ≥ 1200
Therefore the constraints are:
50x + 20y ≥ 2400
30x + 20y ≥ 1200
10x + 40y ≥ 1200
x > 0, y > 0
The graph was drawn using geogebra online graphing tool, and the solution to the problem is at:
C(30, 45) and D(48, 18)
dairy-based meal costs $0.042 per ounce and the vegan option costs $0.208 per ounce. The cost equation is:
Cost = 0.042x + 0.208y
At C(30, 45); Cost = 0.042(30) + 0.208(45) = $10.62
At C(48, 18); Cost = 0.042(48) + 0.208(18) = $5.76
The minimum cost is at (48, 18). That is 48 dairy based meal and 18 vegan
A large truck and a small car traveling at the same speed have a head-on collision. The vehi-cle to undergo the greater change in velocity will be?
Answer:
The car ...Explanation:
Astronauts aboard the ISS move at about 8000 m/s, relative to us when we look upward.How long does an astronaut need to stay aboard the space station to be a full second youngerthan people on the ground? Please show and explain how you would set-up the problem,before you actually try to solve it. If you cannot solve it exactly, please try to offer an estimate.(5 pts)
Answer:
#_time = 7.5 10⁴ s
Explanation:
In order for the astronaut to be younger than the people on earth, it follows that the speed of light has a constant speed in vacuum (c = 3 108 m / s), therefore with the expressions of special relativity we have.
t = [tex]\frac{t_p}{ \sqrt{1- (v/c)^2} }[/tex]
where t_p is the person's own time in an immobile reference frame,
[tex]t_{p} = t \sqrt{1 - (\frac{v}{c})^2 }[/tex]
let's calculate
we assume that the speed of the space station is constant
[tex]t_p = 1 \sqrt{1 - \frac{8 \ 10^3}{3 \ 10^8} }[/tex]
[tex]t_p = 1 \sqrt{1- 2.6666 \ 10^{-5}}[/tex]
t_ = 0.99998666657 s
therefore the time change is
Δt = t - t_p
Δt = 1 - 0.9998666657
Δt = 1.3333 10⁻⁵ s
this is the delay in each second, therefore we can use a direct rule of proportions. If Δt was delayed every second, how much second (#_time) is needed for a total delay of Δt = 1 s
#_time = 1 / Δt
#_time =[tex]\frac{1}{1.3333 \ 10^{-5}}[/tex]
#_time = 7.5 10⁴ s
Two blocks connected by a string are pulled across a horizontal surface by a force applied to one of the blocks, as shown to the right. The mass of the left block m1 = 1.4 kg and the mass of the right block m2 = 4.9 kg. The angle between the applied force and the horizontal is θ = 54°. The coefficient of kinetic friction between the blocks and the surface is μ = 0.38. Each block has an acceleration of a = 3.6 m/s2 to the right.
Answer:
Explanation:The Mass Of The Left Block M1 = 1.3 Kg And The Mass Of The Right Block M2 = 3.1 Kg. The Angle Between The String And The Horizontal Is ... (10%) Problem 8: Two blocks connected by a string are pulled across a horizontal surface by a ... m m, 50% Part (a) Write an equation for the magnitude of the force exerted by the ...
The engine in an imaginary sportThe engine in an imaginary sports car can provide constant power to the wheels over a range of speeds from 0 to 70 miles per hour (mph). At full power, the car can accelerate from zero to 30.0 mph in time 1.00 s .s car can provide constant power to the wheels over a range of speeds from 0 to 70 miles per hour (mph).
Required:
a. At full power, how long would it take for the car to accelerate from 0 to 58.0mph?
b. A more realistic car would cause the wheels to spin in a manner that would result in the ground pushing it forward with a constant force (in contrast to the constant power in Part A). If such a sports car went from zero to 29.0mph in time 1.50s , how long would it take to go from zero to 58.0mph ?
Answer:
a. 1.93 s b. 3 s
Explanation:
a. At full power, how long would it take for the car to accelerate from 0 to 58.0mph?
Since the car accelerates from 0 to 30 mph in 1.00 s, we find its acceleration, a from a = (v - u)/t where u = 0 m/s, v = 30 mph and t = 1.00s = 1/3600 h
So, substituting the values of the variables into the equation, we have
a = (v - u)/t
a = (30 mph - 0 mph)/ 1/3600 h
a = 30 mph × 3600 /h
a = 108000 mph²
So, we find the time it takes the car to accelerate to 58 mph from 0 mph from
t = (v' - u')/a where u = 0 mph, v = 58 mph and a = 108000 mph²
So, substituting the value of the variables into the equation, we have
t = (v' - u')/a
t = (58 mph - 0 mph)/108000 mph²
t = 58 mph/108000 mph²
t = 5.37 × 10⁻⁴ h
t = 5.37 × 10⁻⁴ × 3600 s
t = 1.93 s
b. A more realistic car would cause the wheels to spin in a manner that would result in the ground pushing it forward with a constant force (in contrast to the constant power in Part A). If such a sports car went from zero to 29.0mph in time 1.50s , how long would it take to go from zero to 58.0mph ?
Since the car accelerates from 0 to 29 mph in 1.50 s, we find its acceleration, a from a = (v - u)/t where u = 0 m/s, v = 29 mph and t = 1.05s = 1/3600 h
So, substituting the values of the variables into the equation, we have
a = (v - u)/t
a = (29 mph - 0 mph)/ 1.5/3600 h
a = 29 mph × 3600/1.5 /h
a = 104400/1.5 mph²
a = 69600 mph²
So, we find the time it takes the car to accelerate to 58 mph from 0 mph from
t = (v' - u')/a where u = 0 mph, v = 58 mph and a = 69600 mph²
So, substituting the value of the variables into the equation, we have
t = (v' - u')/a
t = (58 mph - 0 mph)/69600 mph²
t = 58 mph/69600 mph²
t = 8.33 × 10⁻⁴ h
t = 8.33 × 10⁻⁴ × 3600 s
t = 3 s
If 0.5 C charge passes through a wire in 10 seconds, what will be the value of the current flowing through the wire? *
20 mA
30 mA
50 mA
60 mA
Answer:
electric current passing through it will be 50mA
Explanation:
electric current = charge / time
I = Q / TI = 0.5 / 10 I = 0.05 amperecurrent = 0.05 A = 50mA
If 0.5C charge passes through a wire in 10 seconds, then 50mA current is flowing through the wire. Thus, the correct option is C.
What is Electric current?
Electric current is the flow of electricity in an electronic circuit. It is the amount of electricity flowing through a electronic circuit. It is generally measured in amperes (A). The larger the value in amperes, the more electricity is flowing in that circuit.
The formula for calculation of Electric current is:
I = Q/T
where, I = electric current,
Q = amount of charge,
T = time required
Therefore, the current flowing in the wire is:
I = 0.5C/ 10 seconds
I = 0.05 A or 50mA (1mA = 10⁻³A)
Therefore, the correct option is C.
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Imagine a third particle, which we will call a cyberon. It has three times the mass of an electron (3_m). It has a positive charge that is three times the magnitude (3_(qe)) of the charge on an electron. What is the ratio of the speed v_c that the cyberon would have when it reaches the upper plate after being released from rest at position h_0 to the speed ve that the electron would have?
Answer:
The answer is "The last choice".
Explanation:
Please find the complete question in the attachment.
In an external electric field, its electrical energy at positive charge becomes directed to just the electrical domain. Therefore it will speed towards its base plate whenever cyber one is released to rest at h0. It was never going to reach the top plate. Thus, the last choice corrects because in this the cyber-on never reaches its upper stage.
Consider the air over a city to be a box that measures 100 km per side that reaches up to an altitude of 1.0 km. Wind (clean air) is blowing into the box along one of its sides with a speed of 4 m/s. An air pollutant is emitted into the box at a rate of 10.0 kg/s; the pollutant degrades with a rate constant k = 0.20/hr. a. Find the steady state concentration of the pollutant (µg/m3 ) in the box if the air is assumed to be completely mixed. b. If the wind speed suddenly drops to 1 m/s, estimate the concentration of the pollutant (µg/m3 ) two hours later.
Answer:
a) ρ = 6.25 10⁵ μg / m³, b) ρ = 1 10⁷ μg / m³
Explanation:
Let's analyze the exercise a little before starting, we must know the amount of pollutant in the box, that the one that enters less the one that degrades and with this value find the density or concentration.
Let's start by finding the volume of air that goes into the box
V = Lh x
Let's find the distance of air that enters per unit of time, as it goes at constant speed
x = v₀ t
we substitute
V₀ = Lh v₀ t
At this same time, a quantity of pollutant is distributed
Q₀ = r t
the contaminant that is entering reaches the entire box, therefore the total amount of contaminant is
Q = Qo t
we substitute
Q = r t²
the net amount of pollutant that remains is that less enters the one that degraded in the same time, as they ask for the steady state
[tex]Q_{net}[/tex]= Q - k t
the pollutant concentration is
ρ = Q_net / V
V = L L h
ρ =[tex]\frac{r \ t^2 - k \ t}{ L^2 h}[/tex]
ρ = [tex](r \frac{ L^2}{v_o^2} - k \frac{L}{v_o} ) \frac{1}{L^2 h}[/tex]
ρ = [tex]\frac{r}{ v_o h} -\frac{k}{v_o L h}[/tex]
let's reduce the magnitudes to the SI system
r = 10 kg / s
L = 100 km = 100 10³ m
h = 1 km = 1 10³ m
k = dq / dt = 0.20 1/h ( 1h/3600 s) = 5.5555 10⁻⁵ 1/s
v₀ = 4 m / s
let's calculate
The volume of the box
V = (100 100 1) 109
V = 1 10¹³ m³
ρ = [tex]\frac{10}{ 4^2 \ 1\ 10^3 } - \frac{5.5556 \ 10^{-5}}{ 4 \ 100 \ 10^3 1 \ 10^3}[/tex]
ρ = [tex]6.25 10^{-4} - 1.389 ^{-13}[/tex]
ρ = 6.25 10⁻⁴ kg / m³
let's reduce to μg / m³
ρ = 6.25 10⁻⁻⁴ kg / m³ (10⁹ μg / 1kg)
ρ = 6.25 10⁵ μg / m³
b) in case the air speed decreases to v₀ = 1 m / s
ρ= \frac{10}{ 1^2 \ 1\ 10^3 } - \frac{5.5556 \ 10^{-5}}{ 1 \ 100 \ 10^3 1 \ 10^3}
ρ = 1 10⁻² - 5.5556 10⁻¹³
ρ = 1 10⁻² kg / m³
ρ = 1 10⁷ μg / m³
Two blocks collide on a frictionless surface, as shown above. They have a combined mass of 10 kg and a speed of 2.5 m/s. Before the collision, one of the blocks was at rest. This block had a mass of 8 kg. What was the speed of the second block?
Answer:
12.5 m/s
Explanation:
Excuse my scribbles!
I had to work backwards using the inelastic collision formula for this problem.
Formula: V=(M₁V₁+M₂V₂)/(M₁+M₂)V= Combined SpeedM₁= Block 1's MassV₁= Block 1's Velocity M₂= Block 2's MassV₂= Block 2's VelocityStep 1: Substitute in the values provided in the problem
Combined mass: 10kgCombined speed: 2.5m/sBlock 1's mass: 8kgBlock 1's speed: 02.5=(8*0)+(?*?)/(8+?)
Step 2: Subtract block 1's mass from the combined mass to determine block 2's mass
10-8=2 Block 2's mass is 2.
2.5=(8*0)+(2*x)/(8+2)
Now simplify.
2.5=(2*x)/(8+2)
2.5=2x/10
Step 3: Multiply both sides by the reciprocal
(5)2.5=2x/10(5)
12.5=x
Answer is checked in the attached images!
Student pushes a 50 N block across the floor for a distance of 15 m how much work was done to move the block
Answer:
750 J
Explanation:
We have a student that pushes a 50N block across the floor for a distance of 15m. The question is asking how much work was done to move the block.
To solve this, we must know that we are looking for a certain thing called joules. And to get the answer, we must follow the formula of W = FS
F being the force and S being the distance.
W = FS
W = (50)(15)
W = 750
Therefore, 750 joules is our answer.
Which two statements below are central ideas in the article, "How Gross Is Your Bathroom"?
a. What you can't see might hurt you.
b. Different numbers of bacteria are hiding on various surfaces around your bathroom.
c. Most bacteria are harmless, and some are even good for you.
d. Your bathroom is filled with germs that you might not know anything about, including
viruses and bacteria.
What are some technological limitations that currently prevent humans from traveling to distant planets?
Answer:
Propulsion system, antigravitational tech
Explanation:
Fuel is extremely inefficient and expensive not to mention it weighs a lot. You really only need to reach escape velocity to leave earth. The rest is just a little amount of boosting to alter course and slow down for landing. I couldn't really think of much. Once we have an antigravitational system then you could say the whole rocket is holding you back because the design would be different. Nobody really knows how to defy gravity but that would be a technolgical limitation for sure.
it is an organic compound and an essential micronutrient that the body needs in small amounts.
Answer:
Nutrients the body needs in relatively small amounts are called micronutrients. They include vitamins and minerals. Vitamins are organic compounds that are needed by the body to function properly. ... Vitamins and minerals do not provide energy, but they are still essential for good health
Explanation:
The next four questions refer to the situation below.
A person is swimming in a river with a current that has speed vR with respect to the shore. The swimmer first swims downstream (i.e. in the direction of the current) at a constant speed, vS , with respect to the water. The swimmer travels a distance D in a time tOut . The swimmer then changes direction to swim upstream (i.e. against the direction of the current) at a constant speed, vS , with respect to the water and returns to her original starting point (located a distance D from her turn-around point) in a time tIn .
What is tOut in terms of vR, vS, and D, as needed?
Answer:
t_{out} = [tex]\frac{v_s - v_r}{v_s+v_r}[/tex] t_{in}, t_{out} = [tex]\frac{D}{v_s +v_r}[/tex]
Explanation:
This in a relative velocity exercise in one dimension,
let's start with the swimmer going downstream
its speed is
[tex]v_{sg 1} = v_{sr} + v_{rg}[/tex]
The subscripts are s for the swimmer, r for the river and g for the Earth
with the velocity constant we can use the relations of uniform motion
[tex]v_{sg1}[/tex] = D / [tex]t_{out}[/tex]
D = v_{sg1} t_{out}
now let's analyze when the swimmer turns around and returns to the starting point
[tex]v_{sg 2} = v_{sr} - v_{rg}[/tex]
[tex]v_{sg 2}[/tex] = D / [tex]t_{in}[/tex]
D = v_{sg 2} t_{in}
with the distance is the same we can equalize
[tex]v_{sg1} t_{out} = v_{sg2} t_{in}[/tex]
t_{out} = t_{in}
t_{out} = [tex]\frac{v_s - v_r}{v_s+v_r}[/tex] t_{in}
This must be the answer since the return time is known. If you want to delete this time
t_{in}= D / [tex]v_{sg2}[/tex]
we substitute
t_{out} = \frac{v_s - v_r}{v_s+v_r} ()
t_{out} = [tex]\frac{D}{v_s +v_r}[/tex]
Explain how a common housecat gets “worms.”eplain(science)
Answer:
Cats most commonly contract worms after coming into contact with parasite eggs or infected feces. A cat may walk through an area with eggs or infected feces, and since cats are often such fastidious groomers, they will then ingest the eggs or fecal particles as they clean their fur and feet.
Explanation:
this is the only thing in my book hope it helps
Drag the tiles to the correct boxes to complete the pairs
Match the particles with their characteristics.
subatomic particles with a positive charge
subatomic particles with a negative charge
subatomic particles with no charge
made of atoms
neutrons
electrons
protons
malaria
Answer:
1. Protons.
2. Electrons.
3. Neutrons.
4. Molecules.
Explanation:
1. Protons: subatomic particles with a positive charge. They are bound together in the nucleus of an atom due to strong nuclear forces.
2. Electrons: subatomic particles with a negative charge. Electrons can be defined as subatomic particles that are negatively charged and as such has a magnitude of -1.
3. Neutrons: subatomic particles with no charge. The negative charge of the electrons cancels the positive charge of the protons.
4. Molecules: they are made of atoms.
Generally, molecules attach on the inside of a mineral to give it shape. Therefore, the molecule of a mineral is a crystal three-dimensional regular structure (arrangement) of chemical particles that are bonded together and determines its shape.
Due to the fact that these molecules are structurally arranged or ordered and are repeated by different symmetrical and translational operations they determine the shape of minerals.
2. One tin for weight control is to:
Eat alone
Eat slowly
Answer:
Eat slowly
Explanation:
If you eat slower, you'll chew your food better, which leads to better digestion. Digestion actually starts in the mouth, so the more work you do up there, the less you'll have to do in your stomach. This can help lead to fewer digestive problems. Less stress.
PLEASE HELP QUICK which statement describes a primary difference between an electromagnetic wave and mechanical wave?
A. electromagnetic waves can travel through empty space
B. electromagnetic waves can be transverse longitudinal or surface waves
C. electromagnetic waves can only travel through solids liquids or gases
D. electromagnetic waves need a medium to transfer energy
Answer:
A.
Explanation:
An electromagnetic wave is produced by the interaction between a variable electric field, and a magnetic electric field, which propagates in space, even in vaccuum, at a fixed speed, whilst the mechanical waves require a medium in order to transfer energy.Answer: A
Explanation:
It's time to get a little more specific. Based on the velocity (Vx) graph for the car and the velocity data in the table, divide the total
motion of the car into rough time periods that tell a different "chapter" of the story for this car trip. In each of these time
periods, the car's velocity will be notably different from the previous period. Enter a brief description of the car's motion in each
period. The first one is done for you. Use it as an example to identify and describe the remaining time periods. Note: You can
define as many periods as you think appropriate.
s
B
1
U X
X х.
Font Sizes
А • А
E
E 를 들
E 3
Numbered list
Time Period
Motion Description
0.2 - 4.6 seconds increasing speed in positive direction
Answer:
0.2 – 4.6 seconds increasing speed in positive direction
4.6 - 7.8 seconds decelerating speed in a positive direction
8 - 17.2 seconds accelerating speed in a negative direction
Explanation:
**Plato** **Edmentum**n~ this question is pretty open ended, so its hard to get it wrong honestly, good luck <3 ~
Answer:
0.2 – 4.6 seconds increasing speed in positive direction
4.6 - 7.8 seconds decelerating speed in a positive direction
8 - 17.2 seconds accelerating speed in a negative direction
Explanation:
Diagram B D c с Which car has: Ke = 100 PE=0? * 1 point A B C D
Answer:
The car C has KE = 100, PE = 0
Explanation:
The principle of conservation of energy states that although energy can be transformed from one form to another, the total energy of the given system remains unchanged.
The energy that a body possesses due to its motion or position is known as mechanical energy. There are two kinds of mechanical energy: kinetic energy, KE and potential energy, PE.
Kinetic energy is the energy that a body possesses due to its motion.
Potential energy is the energy a body possesses due to its position.
From the principle of conservation of energy, kinetic energy can be transformed into potential energy and vice versa, but in all cases the energy is conserved or constant.
In the diagram above, the cars at various positions of rest or motion are transforming the various forms of mechanical energy, but the total energy is conserved at every point. At the point A, energy is all potential, at B, it is partly potential partly kinetic energy, However, at the point C, all the potential energy has been converted to kinetic energy. At D, some of the kinetic energy has been converted to potential energy as the car climbs up the hill.
Therefore, the car C has KE = 100, PE = 0
2.) The lob in tennis is an effective tactic when your opponent is near the net. It consists of lofting the ball over his/her head, forcing them to move quickly away from the net. Suppose that you loft the ball with an initial speed of 15m/s at an angle of 50 degrees from the horizontal. At this moment your opponent is 10m from the ball. They begin to run away from you 0.3 seconds after the ball was launched hoping to reach the ball and hit it back to you at a height of 2.1m above where you hit it. What is the minimum average speed that your opponent must move so that he is in position to hit this ball
Answer:
The minimum average speed the opponent must move so that he is in position to hit the ball is approximately 5.79 m/s
Explanation:
The given parameters of the ball are;
The initial speed of the ball = 15 m/s
The direction in which the ball is launched = 50° above the horizontal
The location of the other tennis player when the ball is launched = 10 m from the ball
The time at which the other tennis player begins to run = 0.3 seconds after the ball is launched
The height at which the ball is hit back = 2.1 m above the height from which the ball is launched
The vertical position, 'y', at time, 't', of a projectile motion is given as follows;
y = (u·sinθ)·t - 1/2·g·t²
When y = 2.1 m, we have;
2.1 = (15·sin(50°))·t - 1/2·9.8·t²
∴ 4.9·t² - (15·sin(50°))·t + 2.1 = 0
Solving with the aid of a graphing calculator function, we get;
t = 0.199776187257 s or t = 2.14525782198 s
Therefore, the ball is at 2.1 m above the start point on the other side of the court at t ≈ 2.145 seconds
The horizontal distance, 'x', the ball travels at t ≈ 2.145 seconds is given as follows;
x = u × cos(50°) × t = 15 × cos(50°) × 2.145 ≈ 20.682 m
The horizontal distance the ball travels at t ≈ 2.145 seconds, x ≈ 20.682 m
Therefore, we have;
The time the other player has to reach the ball, t₂ =2.145 s - 0.3 s ≈ 1.845 s
The distance the other player has to run, d = 20.682 m - 10 m = 10.682 m
The minimum average speed the other player has to move with, [tex]v_s[/tex] = d/t₂
∴ [tex]v_s[/tex] = 10.682 m/(1.845 s) ≈ 5.78970189702 m/s ≈ 5.79 m/s
The minimum average speed the opponent must move so that he is in position to hit the ball, [tex]v_s[/tex] ≈ 5.79 m/s.
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Answer:
It's A
Explanation:
sound waves are longitudinal they need a medium to travel through
3.
What part of your eye is responsible for regulating the amount of light that enters your eye?
Answer:
Iris
Explanation:
The iris seems to be the illuminated portion of the eyes which really covers the pupil. It controls the amount of light reaching the eye. The lens is indeed a translucent layer of the retina that serves to concentrate light and objects on the lens.
Answer:
I hope this helps.
Explanation:
g Suppose that you seal an ordinary 60W lightbulb and a suitable battery inside a transparent enclosure and suspend the system from a very sensitive balance. (a) Compute the change in the mass of the system if the lamp is on continuously for one year at full power. (b) What difference, if any, would it make if the inner surface of the container were a perfect reflector
Answer:
kekemeeimdeiddnekem
Explanation:
mdjdjdiddmjd jjeneeiej
The force between two charges when they are 2 cm apart is
0.036 N. If the sum of two charges is 10uC, what are the
charges? (1/4ttɛo=9x109 Nm-C-2).
Answer:
[tex]q_1=9.9998\mu C[/tex] and [tex]q_2=0.0002\mu C[/tex]
Or
[tex]q_1=0.00016\mu C[/tex] and [tex]q_2=9.99984\mu C[/tex]
Explanation:
We are given that
Force between two charges=0.036 N=[tex]36\times 10^{-3}N[/tex]
Distance between two charges, r=2cm=[tex]2\times 10^{-2}[/tex]m
1m=100cm
Sum of two charges=[tex]10\mu C[/tex]
Let one charge=[tex]q_1=q\mu C=q\times 10^{-6}C[/tex]
[tex]q_2=(10-q)\times 10^{-6} C[/tex]
We know that
Electric force between two charges
[tex]F=\frac{kq_1q_2}{r^2}[/tex]
Where [tex]k=\frac{1}{4\pi \epsilon_0}=9\times 10^{9}[/tex]
Using the formula
[tex]36\times 10^{-3}=9\times 10^{9}\times \frac{q\times 10^{-6}\times(10-q)\times 10^{-6}}{(2\times 10^{-2})^2}[/tex]
[tex]\frac{144\times 10^{-7}}{9\times 10^{9}\times 10^{-12}}=q(10-q)[/tex]
[tex]0.0016=10q-q^2[/tex]
[tex]q^2-10q+0.0016=0[/tex]
[tex]10000q^2-100000q+16=0[/tex]
[tex]q=\frac{100000\pm\sqrt{(100000)^2-4\times 10000\times 16}}{2\times 10000}[/tex]
Using the formula
[tex]x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
[tex]q=9.999[/tex] and [tex]q=0.00016[/tex]
[tex]q_2=10-9.9998=0.0002[/tex]
[tex]q_2=10-0.00016=9.99984[/tex]
Hence, two charges are
[tex]q_1=9.9998\mu C[/tex] and [tex]q_2=0.0002\mu C[/tex]
Or
[tex]q_1=0.00016\mu C[/tex] and [tex]q_2=9.99984\mu C[/tex]
uppose that the terminal speed of a particular sky diver is 150 km/h in the spread-eagle position and 320 km/h in the nosedive position. Assuming that the diver's drag coefficient C does not change from one position to the other, find the ratio of the effective cross-sectional area A in the slower position to that in the faster position (Aslower / Afaster).
Answer:
4.55
Explanation:
The terminal speed of a diver is given by:
[tex]v_t=\sqrt{\frac{2mg}{C\rho A} } \\\\Where\ m=mass\ of \ driver,d=acceleration\ due\ to\ gravity,C=drag\ \\coefficient,A=cross\ sectional\ Area.\\\\Therefore:\\\\A=\frac{2mg}{C \rho v_t^2} \\\\For\ area\ with\ terminal\ speed\ in\ spread\ angle\ position(v_s):\\\\A_s=\frac{2mg}{C \rho v_s^2} \\\\For\ area\ with\ terminal\ speed\ in\ nose\ dive\ position(v_n):\\\\A_n=\frac{2mg}{C \rho v_n^2}\\\\Therefore\ since\ g,m,C,\rho\ are\ constant:\\\\[/tex]
[tex]\frac{A_s}{A_n}= \frac{\frac{2mg}{C \rho v_s^2}}{\frac{2mg}{C \rho v_n^2}}\\\\\frac{A_s}{A_n}= \frac{v_n}{v_s} \\\\v_n=320\ km/h,v_s=150\ km/h\\\\\frac{A_s}{A_n}=\frac{320^2}{150^2} =4.55[/tex]