Sled slides down a frictionless hill 13.3 m high. At the bottom of the hill the sled hits a long patch of rough snow that slows down the sled by exerting an average force of 170 N on sled. The mass of the sled and rider is 80 kg.

Your initial spot is at the top of the hill.

How fast is the sled going after 10 m down hill

How far must the sled travel before it is traveling 1/3 of its max speed?

How far will the sled slide until it comes to rest?

What would the speed of the sled be at the top of the hill?

Is it realistic?

Potential energy is found by E=mgh where m is the mass, g is the acceleration of gravity and h is the height. Since it's a frictionless hill, all of the potential energy turns into kinetic energy by the time you get to the bottom of the hill. Kinetic energy: E=1/2 mv^2 where again m is the mass, v is the velocity.

Set potential energy equal to kinetic energy and solve for v.

For the second part, F = ma where Force (170 N) = mass times acceleration (or deceleration in this case). You know the force and the mass, you can calculate the deceleration. From that you should easily be able to calculate the rest of the problem.

Speed at the top of the hill? I thought it was assumed to be zero, but quite honestly, we don't know. If there was an initial speed, it will add to the energy at the top, and the bottom of the hill.