A baskeball, with a tennis ball sitting on top of it, is released from rest from
ID: 2245801 • Letter: A
Question
A baskeball, with a tennis ball sitting on top of it, is released from rest from a 2-m vertical height. When they hit the ground the momentum transfer sends the tennis ball flying upward. What is the theoretical final maximim height of the tennis ball? Assume the basketball hits the ground first and changes directions before hitting the tennis ball upward. Finally, assume all collisions are elastic. An elastic collision not only conserves momentum but also kinetic energy (K), so you'll have to simultaneously use momentum conservation with the kinetic energy conservation below to analyze the interaction.
Explanation / Answer
Just before the basketball hits the ground, both balls are moving downward with
speed v0 = sqrt (2*g*2) = 6.2642 m/s
When the basketball bounces off the ground, it moves upward with
speed v0, while the tennis ball still moves downward with speed v0.
The relative speed is therefore 2v0.
assuming, m1>> m2.
after the basketball bounces the center-of-mass frame is moving upwards with velocity
V=v0.
The tennis ball thus has an upwards lab-frame velocity of
2v0+V=3v0. By conservation of energy, it will therefore rise to a height of ,
hf =h+ 3v0^2/2g = 2+3* 6.2642^2/2*9.81
hf = 8 m
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