A tennis ball of mass 57.0 g is held just above a basketballof mass 590 g. With
ID: 1671533 • Letter: A
Question
A tennis ball of mass 57.0 g is held just above a basketballof mass 590 g. With their centers vertically aligned, bothballs are released from rest at the same time, to fall through adistance of 2.00 m.a) Find the magnitude of the downward velocity with which thebasketball reaches the ground.
b) Assume that an elastic collision with the ground instantaneouslyreverses the velocity of the basketball while the tennis ball isstill moving down. Next, the two balls meet in an elasticcollision. To what height does the tennis ballrebound?
A tennis ball of mass 57.0 g is held just above a basketballof mass 590 g. With their centers vertically aligned, bothballs are released from rest at the same time, to fall through adistance of 2.00 m.
a) Find the magnitude of the downward velocity with which thebasketball reaches the ground.
b) Assume that an elastic collision with the ground instantaneouslyreverses the velocity of the basketball while the tennis ball isstill moving down. Next, the two balls meet in an elasticcollision. To what height does the tennis ballrebound?
Explanation / Answer
a) when released, both balls start from rest and fall freely underthe influence of gravity for 1.20 m before the basketball touchesthe ground. their downward speed just before the basketball hitsthe ground may be found fromv2y=v02y+2ayy.This yields:vi=(v02y+2ayy)=[0+2(-9.80m/s2)(-2.00m)]=6.26m/s b) immediately after the basketball rebounds from the floor, it andthe tennis ball meet in an elastic collision. the vertical velocityof each ball just before the collision is: for the tennis ball: v1i=-vi=-6.26m/s for the basketball: v2i=+vi=+6.26m/s the velocity of the tennis ball immediately after this elasticcollision may be found as follows: conservation of momentum gives (57.0g)v1f+(590g)v2f=(57.0g)(-6.26m/s)+(590g)(+6.26m/s) which reduces tov2f=5.66m/s-(9.66x10-2)v1f from the characteristics of a head-on elastic collision, we knowthat v1f-v2f=-(v1i-v2i)=-(-6.26m/s-6.26m/s)=+12.52m/s or v1f=12.52m/s+v2f
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