A skier is traveling at a speed of 36.2 m/s when she reaches the base of a frictionless ski hill. This hill makes an angle of 15° with the horizontal. She then coasts up the hill as far as possible. What height (measured vertically above the base of the hill) does she reach?

h = v²/2g

66.9 To find the height the skier reaches, we can use the principle of conservation of energy.

The initial energy of the skier at the base of the hill is kinetic energy, given by:

KE = 1/2 * m * v^2

where m is the mass of the skier and v is the velocity.

At the top of the hill, the skier reaches a maximum height, where her energy is in the form of potential energy. The potential energy is given by:

PE = m * g * h

where g is the acceleration due to gravity (approximately 9.8 m/s^2) and h is the height above the base of the hill.

According to the principle of conservation of energy, the initial kinetic energy is equal to the final potential energy:

KE = PE

Substituting the equations for KE and PE, we have:

1/2 * m * v^2 = m * g * h

Since the mass of the skier cancels out, we can simplify the equation to:

1/2 * v^2 = g * h

Now, we can solve for h:

h = (1/2) * (v^2 / g)

Substituting the given values:

v = 36.2 m/s
g = 9.8 m/s^2

h = (1/2) * (36.2^2 / 9.8)

Calculating this equation gives us the height the skier reaches.