A 60.0 kg skier rides a 2710 m long lift to the top of a mountain. The lift makes an angle of 14.5° with the horizontal. What is the change in the skier's gravitational potential energy?
To calculate the change in the skier's gravitational potential energy, we need to determine the vertical distance the skier has moved. We can use trigonometry to find this distance.
First, we find the vertical component of the distance traveled by multiplying the total distance by the sine of the angle of the lift with the horizontal:
Vertical distance = 2710 m * sin(14.5°)
Now, we can calculate the change in gravitational potential energy using the formula:
Change in gravitational potential energy = mass * gravitational acceleration * vertical distance
The mass of the skier is given as 60.0 kg, and the gravitational acceleration can be approximated as 9.8 m/s².
Change in gravitational potential energy = 60.0 kg * 9.8 m/s² * vertical distance
Now, let's substitute the calculated vertical distance into the equation and solve for the change in gravitational potential energy.