Acertain ball has the property that each time it falls from aheight h onto a hard level surface, it rebounds to aheight rh, where 0 < r < 1. suppose thatthe ball is dropped from an initial height h meters.
a)assuming that the ball continues to bounceindefinitely, find the total distance that it travels. (use the fact thatthe ball falls (1/2)gt2 meters in tseconds)
b)calculate the total time that the balltravels.
c)suppose that each time the ball strikes thesurface with velocity v it rebounds with velocity -kv, where0 < k < 1. how long will it take for the ball tocome to rest?

a)

b)

c) The ball never gets velocity 0.

Step-by-step explanation:

a)

Assuming the initial height is H meters we have the total distance traveled is  

H + distance traveled 1st bounce +  distance traveled 2nd  bounce+ distance traveled 3rd  bounce +...(and so on)

The distances traveled in each bounce are

So, the total distance traveled is

but  

is a convergent geometric series (without the first term=1) which converges to

and we have that the total distance traveled is

b)

Since the total time t traveled by the ball is given by the second equation of motion

we then have

and finally

c)

At bounce number n the velocity would be and we know  

for 0 < k < 1.

So, theoretically speaking, the ball will never have velocity zero, but will become smaller and smaller until it becomes zero in the infinite.

the entire expression should be subtracted from 30. to subtract the quantity, distribute the negative sign, which changes the signs on the terms. so, the –2 changes to positive and gets added to 30 instead of subtracted from it.

hope this ! ^w^