A skier with a mass of 60.0 kg starts from rest and skis down an icy (frictionless) slope that has a length of 53.0 m at an angle of 25.4° with respect to the horizontal. At the bottom of the slope, the path levels out and becomes horizontal, the snow becomes less icy, and the skier begins to slow down, coming to rest in a distance of 137 m along the horizontal path. What is the speed of the skier at the bottom of the slope?

sin25.4 = h/53, h = 53*sin25.4 = 22.7 m.

PE = M*g*h = 60*9.8*22.7 = 13,367 J.

KE = PE, 0.5M*V^2 = 13,367, 30*V^2 = 13367, V = 21.1 m/s. = Velocity at bottom of slope.

To solve this problem, we can use the principles of conservation of energy. We know that the gravitational potential energy at the top of the slope is converted into kinetic energy at the bottom of the slope.

The initial potential energy of the skier at the top of the slope can be calculated using the formula:

Potential energy = mass * acceleration due to gravity * height

First, let's calculate the height of the slope using the given angle:

height = length of the slope * sin(angle)

height = 53 m * sin(25.4°)

Next, let's calculate the potential energy at the top of the slope:

Potential energy = 60.0 kg * 9.8 m/s^2 * height

Now, since there is no friction, this potential energy is converted into kinetic energy at the bottom of the slope:

Initial potential energy = Final kinetic energy

60.0 kg * 9.8 m/s^2 * height = 0.5 * mass * velocity^2

We only need to solve for the velocity at the bottom of the slope. Rearranging the equation, we get:

velocity = √(2 * (60.0 kg * 9.8 m/s^2 * height) / mass)

Substituting the values we calculated earlier, we can find the velocity at the bottom of the slope.