A novice skier starts from rest and slides down a frictionless 35 degree incline whose height is 125 m. How fast will she be going at the bottom?

I'm not sure if this is right but my answer was 49.50 for the skier

Velocity 49.50

mgh=1/2 mv^2

v=sqrt(2gh)=sqrt(2*9.8*125)
that agrees with your answer

To find the speed of the skier at the bottom of the incline, we can use the principle of conservation of energy. Here's how to solve it step by step:

Step 1: Determine the change in potential energy (PE).
The change in potential energy is equal to the initial potential energy (at the top of the incline) minus the final potential energy (at the bottom of the incline).
The formula for potential energy is given by PE = m * g * h, where m is the mass, g is the acceleration due to gravity, and h is the height. In this case, we know h = 125 m.

Step 2: Calculate the change in potential energy.
Since the skier starts from rest, the initial potential energy (PEi) is equal to the mass times the height, which can be written as PEi = m * g * h.
The final potential energy (PEf) is zero because the skier is at the bottom of the incline, where the height is zero.

So, the change in potential energy (ΔPE) = PEf - PEi = 0 - (m * g * h).

Step 3: Convert the change in potential energy to kinetic energy.
According to the conservation of energy, the change in potential energy is converted to kinetic energy. The formula for kinetic energy is given by KE = (1/2) * m * v^2, where v is the speed or velocity of the skier.
Equating the change in potential energy to the kinetic energy, we get ΔPE = KE, which can be written as m * g * h = (1/2) * m * v^2.

Step 4: Solve for the velocity (v).
Rearrange the equation to solve for v. Divide both sides of the equation by (1/2) * m:
v^2 = (2 * g * h).
Now, take the square root of both sides of the equation: v = sqrt(2 * g * h).

Step 5: Substitute the known values and calculate.
Substitute the known values for g (acceleration due to gravity) and h (height) into the equation:
v = sqrt(2 * 9.8 m/s^2 * 125 m).
Calculate the value to get the speed of the skier at the bottom of the incline.

After following these steps and performing the calculations, you will find the speed at which the novice skier will be going at the bottom of the incline.