Ball dropped out a truck window, find bounce height and dist

In summary, the conversation discusses the calculation of the height and horizontal distance of a ball dropped out of a moving truck, with a given weight and coefficient of restitution. The participants discuss different equations and methods for finding the first bounce height and horizontal velocity after the bounce, as well as the time and distance for the ball's second bounce. The conversation also touches on the use of the coefficient of restitution and its impact on the ball's energy and height.
  • #1
jbm1939
7
1

Homework Statement


A ball weighing 0.2 lbs is dropped out the window of a pickup truck moving horizontally at 45 mph. If the C.O.R. (e) between the ball and the ground is equal to 0.6, find the height of the ball's first bounce and the horizontal distance it will travel before bouncing again.

I believe i have the height of the bounce, but am stuck on how far it will travel horizontally. I'll put below what i have so far.

The attempt at a solution:

mgh = 1/2mv2
Vf = Square rt(2gh)
square rt(2(32.2)(5ft)
=17.9 ft/s

V1 = 0.6(17.9ft/s)
= 10.76 ft/s

1/2mv2 = mgh
h=vi2 / 2g
=10.762 / 2(32.2)
=1.798 ft
 
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  • #2
You can get the bounce height a bit more easily, it's just the original times the square of the coefficient.
What is the horizontal velocity after the bounce? What else do you need to figure out to find the distance to the next bounce?
 
  • #3
Now you have found v1 right. From now on

1/2*g*t^2= v1 ===> with that you find the t value ( the time the ball will go upwards)

Then find 2t ( the time ball will bounce upwards and fall back down)

2t* 45 mph = the distance your ball travel before its second bounce. Hope it was helpful and i didnt write something wrong by mistake
 
  • #4
Does anyone know if I found the first height correctly? Another student told me that you just take the orignal height times e to get that. That seems to simple to me but I could be wrong. So in this case it would be 0.6 x 5ft = 3ft
 
  • #5
jbm1939 said:
Does anyone know if I found the first height correctly? Another student told me that you just take the orignal height times e to get that. That seems to simple to me but I could be wrong. So in this case it would be 0.6 x 5ft = 3ft
A quick trip to google indicates that the coefficient of restitution is a ratio of energy, not of velocity. Post #2 assumed the opposite.
Scratch that. I read too quickly. It is a ratio of speed.

If energy goes down by a factor of 0.6 then potential energy at the top of the bounce must go down by a factor of 0.6 and height at the top of the bounce will go down by a factor of... what?

Scratch that. Re-read post #2.
 

1. What is the equation for calculating the bounce height of a ball dropped out of a truck window?

The equation for calculating the bounce height is h = (e^2 * h0), where h is the bounce height, e is the coefficient of restitution (a measure of bounciness), and h0 is the initial drop height.

2. How do you determine the coefficient of restitution for a ball?

The coefficient of restitution can be determined by dropping the ball from a known height onto a hard surface and measuring the rebound height. The coefficient of restitution is then calculated by dividing the rebound height by the initial drop height.

3. What factors can affect the bounce height of a ball?

The bounce height of a ball can be affected by the material and shape of the ball, the surface it bounces on, and the initial drop height and velocity of the ball.

4. Is there a maximum bounce height for a ball dropped out of a truck window?

Yes, there is a maximum bounce height for a ball dropped out of a truck window. This maximum height is determined by the initial drop height, coefficient of restitution, and the height of the truck window.

5. How do you calculate the distance traveled by the ball after it bounces out of the truck window?

The distance traveled by the ball can be calculated using the equation d = h + (h * e^2), where d is the total distance traveled, h is the bounce height, and e is the coefficient of restitution.

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