## Answers to midterm 3 version A (white)

- a
- c
- e
- d
- b
- d = 0.28 m
- theta = 14.8 degrees

## Answers to midtemr 3 version B (yellow)

- a
- b
- a
- b
- e
- d = 0.43 m
- theta = 13.1 degrees

For number 6 conserve momentum mV = (m+M)u and then conserve
energy (even though the collision is inelastic you know where the
extra energy went; into compressing the spring) 1/2 mV^{2} =
1/2(m+M) u^{2} + 1/2 k d^{2}.

7: A piece of clay falling into two chunks is an inelastic process so you
can only conserve momentum to solve this problem. It is a two-dimensional
decay, so you need to write the equations for the x and y directions.
This gives 2 equations for 2 unknowns (M and theta). Use m1i = M+1kg
, m1f = 1 kg, m2f = M, eliminate M. The resulting equation looks like
A sin(theta) = cos(theta) - B, where A and B are known numbers. Square
this and use 1 = sin^{2} + cos^{2} to get a quadratic
equation for cos(theta):

-(1+A^{2})cos^{2} + 2 B cos + A^{2} - B^{2} =0

Finally, solve this for cos(theta).