speed at the bottom of the hill

Question

Sledge goes down a hill that is at 12° degree angle and it is 25 meters long. The starting speed is 0 and there is no friction or air resistance. What is the speed at the bottom of the hill?

Answer 1

For this you can use conservation of energy because all the potential energy

at the top of the hill gets converted to the kinetic energy at the bottom.

Let

m be the mass of the sledge (unknown),

α = 12° be the angle of the hill,

L = 25m be the length of the hill,

h = Lsin(α) be the height of the hill,

v be the speed at the bottom of the hill (to be calculated),

g = 9.81 m/s² be gravitational acceleration.

The potential energy at the top of the hill with respect to the bottom is

mgh

The kinetic energy at the bottom of the hill is

mv²/2

By conservation of energy

mv²/2 = mgh

From that express v

v = √2gh = √2gLsin(α)

Substituting actual numbers

v = √(2×9.81×25×sin(12°)) = 10m/s