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?
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To find the change in the skier's gravitational potential energy, we first need to calculate the change in height.
We can use trigonometry to determine the vertical component of the displacement. The vertical displacement is equal to the length of the lift multiplied by the sine of the angle it makes with the horizontal.
Vertical displacement = Length of the lift × sin(angle)
Vertical displacement = 2710 m × sin(14.5°)
Calculating the vertical displacement:
Vertical displacement = 2710 m × 0.2474
Vertical displacement ≈ 670.45 m
Now, we can calculate the change in gravitational potential energy using the formula:
Change in gravitational potential energy = mass × acceleration due to gravity × change in height
Given:
mass (m) = 60.0 kg
acceleration due to gravity (g) = 9.8 m/s^2
change in height = vertical displacement = 670.45 m
Calculating the change in gravitational potential energy:
Change in gravitational potential energy = 60.0 kg × 9.8 m/s^2 × 670.45 m
Change in gravitational potential energy ≈ 397,478 J
Therefore, the change in the skier's gravitational potential energy is approximately 397,478 J.