A tennis ball of mass 57.0 g is held just above a basketball ofmass 630 g. With
ID: 1672033 • Letter: A
Question
A tennis ball of mass 57.0 g is held just above a basketball ofmass 630 g. With their centers verticallyaligned, both balls are released from rest at the same time, tofall through a distance of 1.35 m, asshown in the figure below.
A tennis ball of mass 57.0 g is held just above a basketball ofmass 630 g. With their centers verticallyaligned, both balls are released from rest at the same time, tofall through a distance of 1.35 m, asshown in the figure below.
A tennis ball of mass 57.0 g is held just above a basketball ofmass 630 g. With their centers verticallyaligned, both balls are released from rest at the same time, tofall through a distance of 1.35 m, asshown in the figure below. (b) To what height does the tennis ballrebound?
2 m
The answer for this and an explanation with how you got it would beimmensely appreciated. Thank you!
Explanation / Answer
The basketball will rebound with a velocity (about) equal to thatat which it struck the ground: 5.14 m/s. Now the tennis ball collides. Momentum is always conserved,and since the collision is elastic, kinetic energy isconserved: I'll use subscripts b for basketball and t for tennis ball, and tomake subscripts easier to read, the terms on the left side of theequals sign are for before the b - t collision, and the terms onthe right side are for after the collision. Conservation of energy: (1/2)mbvb2 +(1/2)mtvt2 =(1/2)mbvb2 +(1/2)mtvt2 Conservation of momentum: mbvb +mtvt = mbvb +mtvt Now you have two equations and two unknowns: - You know all the masses; and they don't change - You know the initial velocity of the basketball ( +5.14m/s; going upward) - You know the initial velocity of the tennis ball ( -5.14m/s; going downward) - You don't know the final velocity of the basketball or thetennis ball Use those two equations to solve for your two unknowns; it shouldonly be a matter of doing some algebra. Then, you will have avalue for the final velocity of the tennis ball. From there,you can figure out how high it goes using the equation: v2 = v02 + 2a(y) v = 0 (since we go to maximum height) v0 = the velocity you found for thetennis ball a = -9.8 m/s2 y = what you are solving for And...what you find for y will be your answer. Note that your answer will probably be greater than the height thatyou started at. If you think that the height you get isunrealistic, try doing this sometime...you might be surprised athow high the tennis ball goes!
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