Momentum and Energy Conservation in Collision Problems

[AverteProxy]

Homework Statement

Had a test today and had to do these problems. I just want confirmation on whether or not I did it correctly.

(One) A sledder is at the top of a (frictionless) hill. He has an initial velocity of 5m/s, and his weight with the sled is 30 Kg.

B) What his his velocity at the bottom of the hill?
c) At the bottom of the hill, the sledder collides in an elastic collision with a 90kg rock. What is the velocity of the rock after the collision?

(Two) A hockey puck hits a wall perpendicularly with a momentum of 2.5 Kg-m/s and rebounds with the exactly same speed. What is the overall change of momentum?

Homework Equations

P = mv
(1/2)Kv^2
PE = MGH

The Attempt at a Solution

On the first part, I set KE = to PE and did this to find the final velocity:

$\frac{1}{2}$mv^2 = mgh

Masses cancel out and I'm left with $\frac{1}{2}$v^2 = gh

After working it out, I end up getting 19.8 m/s. Problem is, I don't know whether or not I would add the initial velocity to this answer.

After, I set KE of the sledder equal to the KE of the rock (elastic collision) and solved for the final velocity of the rock, and somehow get 11 m/s. Would this be correct?

For the second problem, It was multiple choice, and I chose 5. Because it's going 2.5 one direction, and then rebounds to go -2.5 in the opposite direction with equal magnitude. Would 5 be correct? Thanks

 

[Delphi51]

You can't just add the 5 m/s onto the answer. Rather, include the KE of the 5 m/s in the original calc:
energy at top = energy at bottom
mgh + ½m⋅v² = ½m⋅V²

The method for (b) is flawed, too. An elastic collision does not necessarily transfer all of the energy from one object to the other. Elastic just means no kinetic energy is lost. So you should use conservation of momentum AND conservation of energy to figure out the velocities of the masses after the collision. You need TWO equations to find TWO unknowns.

You got the second question right!