What Is the Maximum Height Achieved by Mass M1 After Elastic Collision?

[mshiddensecret]

Homework Statement

Two spheres of mass M1 and M2 are arranged one above the other as shown. They are separated by a fraction of a mm. They are released from rest and allowed to fall to the ground, a distance h = 5.0 m below. Mass M2 collides elastically with the ground and then elastically with mass M1. Calculate the maximum height the center of M1 rises above the ground after the collision. D = 0.20 cm, d = 0.05 cm, M1 = 0.20 kg, M2 = 1.10 kg.

Homework Equations

The Attempt at a Solution

so I got the velocity by using vf^2 = 2ad and got 9.89m/s.

I use the collision formula:

(9.89)(1.1)=(.2)(v)

v= 54.337 - 9.89
=44.557 m/s for the smaller ball.

then 0=44.557^2+2ad

d=101.29 + 5 m = 106m.

Its incorrect.[/B]

 

[NascentOxygen]

It's a bit tricky, so I'd prefer to know the textbook's answer before I venture to offer guidance. ☺

But I think the interaction is between M1 coming down at some speed and colliding with M2 traveling upwards. I think that's what the authors must be intending, anyway.

 

[rude man]

Use potential energy conservation.
(I assume M1 originally sits on top of M2. You should also define d and D though I imagine they are the diameters of M1 and M2 respectively).

 

[haruspex]

I assume that the balls are so small compared to the distance dropped that we can effectively treat them as point masses.

I use the collision formula:
(9.89)(1.1)=(.2)(v)

What formula is that, exactly? What does it apply to? What are the velocities of the two balls immediately before they collide?