Posted by A on .
Gayle runs at a speed of 3.80 m/s and dives on a sled, initially at rest on the top of a frictionless snow covered hill. After she has descended a vertical distance of 5.00 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 15.0 m? Gayle's mass is 50.0 kg, the sled has a mass of 5.00 kg and her brother has a mass of 30.0 kg.

Physics 
bobpursley,
1. figure with conservation of momentum the initial velocity of gayle/sled
2. Now, with conservation of energy, the speed at bottome of hill.
KEbottom=KEattop+PEtop
1/2(Mg+ms)vbottom^2=1/2(Mg+ms)Vtop^2 + (Mg+Ms)g*height
figure vbottom.
Now, with conservation of momentum, figure the new velocity with brother on back.
Then, at the bottom of the hill, figure new velocity with conservation of energy, as before on the first hill.