Question

A certain ball has the property that each time it falls from a height h onto a hard, level surface, it rebounds to a height rh, where 0 < r < 1. Suppose that the ball is dropped from an initial height of H meters. (a) Assuming that the ball continues to bounce indefinitely, find the total distance that it travels. (b) Calculate the total time that the ball travels. (Use the fact that the ball falls 1 2 gt2 meters in t seconds.)

Answer 1

Answer:

a)$S=h\dfrac{1+r}{1-r}$

b)$t=\sqrt{\dfrac{2h}{g}\times \dfrac{1+r}{1-r}}$

Explanation:

a)The total distance

S= h+ 2rh + 2r²h+2³rh+--------∞

S= 2h( 1 + 2 r + 2r² +   ----∞ ) - h

By using summation series

$S=\dfrac{2h}{1-r}-H$

$S=h\dfrac{1+r}{1-r}$

b)

We know that

$y=ut+\dfrac{1}{2}gt^2$

$S=\dfrac{1}{2}gt^2$

By putting the value of S

$h\dfrac{1+r}{1-r}=\dfrac{1}{2}gt^2$

$t=\sqrt{\dfrac{2h}{g}\times \dfrac{1+r}{1-r}}$