A novice skier, starting from rest, slides down a frictionless 29.0∘ incline whose vertical height is 185 mm. How fast is she going when she reaches the bottom?

Her speed when she reaches the bottom of the incline is 1.90 m/s.

Explanation:

Hi there!

To solve this problem, let's use the energy conservation theorem:

Initially, the skier is at rest at a height of 0.185 m. Since she is at rest, her kinetic energy will be zero and her gravitational potential energy (PE) will be:

PE = m · g · h

Where

m = mass of the skier.

g = acceleration due to gravity.

h = height.

When she reaches the bottom, the height is zero and then the potential energy will be zero. Since there is no friction, the initial potential energy had to be converted into kinetic energy because the total energy of the skier remains constant, i. e., it is conserved.

Then, the final kinetic energy (KE) of the skier has to be equal to the initial potential energy:

PE = KE

The equation of kinetic energy is the following:

KE = 1/2 · m · v²

Then:

KE = PE

1/2 · m · v² = m · g · h

1/2 · m · v² = m · 9.8 m/s² · 0.185 m

v² = 2 · 9.8 m/s² · 0.185 m

v = 1.90 m/s

Her speed when she reaches the bottom of the incline is 1.90 m/s.