Question

at the local ski slope, an 82.0-kg skier rides a gondola to the top of the mountain. if the lift has a length of 2950 m and makes an angle of 13.1∘ with the horizontal, what is the change in the gravitational potential energy of the skier–Earth system?

Answer 1

The change in gravitational potential energy of the skier-Earth system is calculated using GPE = mgh, resulting in approximately 532446.34 joules as the skier ascends to the top of the mountain.

Step-by-step explanation:

To calculate the change in the gravitational potential energy of the skier-Earth system as the skier rides a gondola to the top of the mountain, we can use the formula for gravitational potential energy (GPE), which is GPE = mgh. Here, m is the mass of the skier, g is the acceleration due to gravity (9.80 m/s² on the surface of the Earth), and h is the height gained.

First, we need to calculate the height (h) gained by the skier using the length of the ski lift (L) and the angle with the horizontal (θ):

h = L * sin(θ)

h = 2950 m * sin(13.1°)

h = 2950 m * 0.227

h = 669.65 m (approximately)

Now calculate the change in gravitational potential energy:

GPE = mgh

GPE = 82.0 kg * 9.80 m/s² * 669.65 m

GPE = 532446.34 J

Therefore, the change in gravitational potential energy for the skier as they reach the top of the slope is approximately 532446.34 joules.