Expert: Abe Mantell - 2/4/2005

Question
let say at t=0, a ball was dropped from a height of 16ft.  it hit the ground and rebounded to a height of 9ft.
a)find a two part formula for the velocity v(t) that is valid until the ball hits the floor a second time
b) at what two times was the ball at height 9ft.

Answer
Hello Danielle,

for the first part (from 16 ft drop to the floor):
v1(t)=-32t, 0<=t<=t1, t1=time until ball hits floor
for the second part (from the floor to 9 ft to floor again)
v2(t)=-32T+Vo, t1<T<t2,
where t2=time until ball hits floor 2nd time, and
Vo=the intial speed of the ball on the bounce, which
can be determined by knowing the height achieved was
9 ft...same as dropping the ball from 9 ft height and
calculating the speed upon impact (just change in sign)...
Once you do that, then you can figure out all times
involved...

OK?

Abe