Question

a tennis ball bounces down a flight of stairs striking each step in turn and rebounding to the height of the step above if the height of each step is D the coefficient of restitution is​

Answer 1

Explanation:

Using the third equation of motion, we get V initial = (2gh)(1/2) (As the ball falls a distance h above the next step.)

Also, V final = {2g(h-d)}(1/2) (The ball rises a height (h-d) above the step it strikes.)

Using the formula of coefficient of restitution,

we get

(h-d)/h=e2 ( the velocity of steps will be zero)

Rearranging,

h/d=1/(1-e2)

Answer 2

Given:

Tennis ball bouncing down

Height of each step = D

To Find:

Coefficient of restitution

Solution:

Coefficient of restitution = e = vsep/vapp

The conservation of energy for each flight is kept between points of reaching the ground and the point of maximum elevation.

= 1/2 mv²app = mgh

= 1/2 v²sep = mgh/2

= vsep/vapp = 1/√2

e = 1/√2

Answer: The coefficient of restitution is 1/√2