you know mass of cannonball and velocity, thus you know the Kinetic Energy (KE).
this is equal to the KE of the cannon moving in the opposite direction. you know the mass, thus you know the velocity (initial) of the cannon.
you know the weight of the cannon. you know coeffiecient of friction (assume to be dynamic CoEf.) Thus you know the force of friction operating in the opposite direction of the cannon motion. If you know force and mass, you know acceleration. If you know acceleration, you know what speed it'll be going when it hits the hill 50 meters away (one of the basic kinematics equations)
You know velocity of cannon at base of the hill. Along with the mass, you know it's KE at the base of the hill. That's gonna be equal to the potential energy the cannon has when it's at the top of the roll. And since you know it has an eleven degree slope, finding the distance it rolls up is pretty trivial.
problem 2:
For the first 15meters, she pushes with 1.5 times her weight. You know her mass, you know g, thus you know her weight. Multiply by 1.5, you know the force F.
F=ma Thus you know a, acceleration.
you know acceleration for a given distance, thus you know her final velociy at the end of 15 meters, and you know the time it took her to do those 15 meters.
using final velocity as the speed for the rest of the race (485 meters) you know the rest of the time.
add the two times together and you're done.
I think i did em right.. correct me if i didn't
-patchy