Weird Physics Question? please help urgent!

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Weird Physics Question? please help urgent!



This is quite a dramatic collision. 
You drop a small ball on top of a large ball from rest at a height ,h (from ground to right below the large ball) . In this question you will calculate how high the small ball will bounce up. Assume all collisions are elastic so that you can use: 
(Va - Vb)before= -(Va'-Vb')after 

a) What is the velocity of the small ball just when the large ball hits the floor? 

b) What is the velocity of the large ball just after it leaves the floor? 

c) Now the balls collide (after the large ball hits the floor). Use the conservation of momentum and that 
the collision is elastic to solve for the velocity of the small ball after the two balls collide. Assume that the mass of the large ball is much greater than the mass of the small ball so that you can ignore all terms involving the mass of the small ball. 

d) Given the velocity of the small ball just after the collision with the large ball found in (c), how high will 
it go in the air? Now you will use your result from (a) to find out how high it will go in terms of the initial drop height, h

Update: the balls are not together when dropped.



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Posted Answers:

(a) Both balls drop distance h from rest. What is their final downward speed? 
The simplest approach is to use conservation of energy to find the speed that the small ball attains when all of its gravitational potential energy has been converted to kinetic energy. 

(b) Assume the floor doesn't move (it is attached to the Earth, which does not noticeably change velocity due to the impact of a couple of balls). After an elastic collision, what is the large ball's new velocity? 

(c) The large ball is now traveling upwards and the small ball is still falling downwards, with the velocities you calculated in (b) and (a). They collide elastically. 
Now the large ball takes the same role that the Earth did in (b): assume that it does not change velocity as a result of this tiny impact. Thus, what is the small ball's final speed? 

The instruction to "use conservation of momentum," combined with neglecting the small ball's mass, means that the motion of the large ball doesn't change. Do not actually set up equations with 0 mass. Only use the given ΔVi = -ΔVf.