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Ball falls from height strikes floor of lift with velocity 10 if the lift moves upward with velocity 1m/s find the velocity with which the ball rebounds

Ball falls from height strikes  floor of lift with velocity 10 if the lift moves upward with velocity 1m/s find the velocity with which the ball rebounds 

Grade:12th pass

2 Answers

Vikas TU
14149 Points
4 years ago
Dear student 
since the lift is moving upward in the given problem, u1 is positive (+10 m/s)and u2 is negative(-1 m/s)
For elastic collision
m1u1+m2u2=m1v1+m2v2
m1u1^2/2+m2u2^2/2=m1v12/2+m2v2^2/2
solving these two equations, we may get
v1=(-m2u1+2m2u2)/m2
since the lift is moving upward
V1 =(-m2*10+2m2*(-1))/m2
So that V1= -12 m/s
Arun
25750 Points
4 years ago
We consider initial velocity of the ball as u1=-10 m/s with reference to ground, We have taken downward direction as negative. The initial velocity of lift is u2=1m/s. After the collision let the velocities be v1 and v2. Since collision is elastic ,the coefficient of restitution e=1. 
Then,  1=(v1-v2)/(u2-u1) or u2-u1=v1-v2. Putting values of u1 and u2 and taking v2=u2 as lift is very heavy, we have ,  v1=2+10=12m/s for observer on ground.
For observer in the lift the lift is stationary and velocity of the ball before and after collision has same value with reversed direction . So, answer for that observer will be 10 m/
 

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