A basketball, with a tennis ball sitting on top of it, is released from rest fro

Question

A basketball, with a tennis ball sitting on top of it, is released from rest from a 2-m vertical height. (Try this) When they hit the ground the momentum transfer sends the tennis ball flying upward. What is the theoretical final maximum height of the tennis ball? Assume the basketball hits the ground first and changes directions before hitting the tennis ball upward. Finally, as- sume all the collisions, are elastic. An elastic collision not only conserves momentum but also kinetic energy (K), so you A basketball, with a tennis ball sitting on top of it, is released from rest from a 2-m vertical height. (Try this) When they hit the ground the momentum transfer sends the tennis ball flying upward. What is the theoretical final maximum height of the tennis ball? Assume the basketball hits the ground first and changes directions before hitting the tennis ball upward. Finally, as- sume all the collisions, are elastic. An elastic collision not only conserves momentum but also kinetic energy (K), so you

Explanation / Answer

just before hitting the ground both balls are moving downward with speed,

vo=sqrt(2*g*h)

=sqrt(2*9.8*2)

=6.2642 m/sec

here,

the basketball bounces off the ground with speed vo(upward)

and

the tennis ball still moves with speed vo(downward)

the relative speed is 2*v

for the basket ball the center of mass frame is moves the speed v=vo(upward).

there fore,

the tennis ball has an upwards lab-frame velocity is,2vo+V=3vo

by using the energy conservation

tha height rised is,

hf=h+3*vo^2/2*g

hf=2+3*6.2642^2/2*9.8

hf=8 m .....is answer

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