Question

On a snowy day a teen goes tobogganing. The teen pushes the tobbogan with an initial velocity of 1.0 m/s and it begins to slide down a bumpy hill as shown. If the height of the hill is 15 m what is the velocity of the toboggan at the bottom of said hill? Ignore friction.

Answer 1

Without friction the motion will be completely controlled by gravity. At initial stage the total energy of the cart is in the form of the potential energy due to height and kinetic energy due to initial velocity. But once the cart reaches the bottom the total energy is in the form of kinetic energy. By the conservation of energy we can put the two together and solve it for velocity.

Mgh +1/2×mv^2 =m(9.8×15+0.5×1^2)= 147.5×m

Final energy = 1/2×m×v^2

Put these two equal and the mass will cancel out and velocity will solve to v=17.17 m/s