Help finding speed

1. Oct 18, 2009

VelvetRebel

1. The problem statement, all variables and given/known data

Gayle runs at a speed of 4.23 m/s and dives on a sled, which is initially at rest on the top of a frictionless snow-covered hill. After she has descended a vertical distance of 5.03 m, her brother, who is initially at rest, hops on her back and together they continue down the hill. What is their speed at the bottom of the hill if the total vertical drop is 14.1 m? Gayle's mass is 46.8 kg, the sled has a mass of 4.95 kg and her brother has a mass of 26.9 kg.

2. Relevant equations
conservation of momentum

3. The attempt at a solution

I have no idea where to start. I don't understand on where to incorporate the height into the problem. All I know is that you have to apply the conservation of momentum somewhere. I'm also assuming this is a totally inelastic situation.

2. Oct 18, 2009

Pengwuino

Yes, you will use conservation of momentum but determining the speeds upon "collision" will require conservation of energy to determine her/their speeds at various heights on the mountain. You need to determine her speed right before her little brother jumps on, and she will increase her speed due to her change in potential from the top.

3. Oct 18, 2009

VelvetRebel

Oh wow. That was really simple. Thanks for the help.