The change in the skier's gravitational potential energy is 428,092 Joules.
The Breakdown
To calculate the change in the skier's gravitational potential energy, we need to consider the change in height as the skier rides the lift to the top of the mountain.
The change in gravitational potential energy (ΔPE) can be calculated using the formula:
ΔPE = m × g × Δh
where m is the mass of the skier, g is the acceleration due to gravity, and Δh is the change in height.
Given:
m = 60.0 kg (mass of the skier)
g = 9.8 m/s² (acceleration due to gravity)
Δh = height difference
To find the height difference, we can use trigonometry. The vertical height (h) can be calculated using the formula:
h = length × sin(angle)
where length is the length of the lift and angle is the angle it makes with the horizontal.
Given:
length = 2810 m
angle = 14.9°
h = 2810 m × sin(14.9°)
h ≈ 727.9 m
Now we can calculate the change in gravitational potential energy:
ΔPE = 60.0 kg × 9.8 m/s² × 727.9 m
ΔPE ≈ 428,092 J
Therefore, the change in the skier's gravitational potential energy is 428,092 Joules.