A 75.0 kg skier rides a 2870 m long lift to the top of a mountain. The lift makes an angle of 14.4° with the horizontal. What is the change in the skier's gravitational potential energy?
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Find out how much he rises in elevation, using trig, and multiply that by M g.
To calculate the change in the skier's gravitational potential energy, we need to first determine the change in height.
The change in height can be calculated using the given angle and the length of the lift. In this case, the length of the lift is 2870 m, and the angle is 14.4°.
We can use trigonometry to find the height change. The formula to calculate the height change can be derived from the right triangle formed by the lift and the vertical height.
The formula is as follows:
Height change = Length of the lift * sin(angle)
Let's substitute the given values into the formula:
Height change = 2870 m * sin(14.4°)
Next, we need to calculate the sin(14.4°). To do this, you can use a scientific calculator or an online calculator.
Sin(14.4°) ≈ 0.2473
Now, we can substitute this value into the height change formula:
Height change ≈ 2870 m * 0.2473
Height change ≈ 709.831 m
The height change is approximately 709.831 m.
Finally, we can calculate the change in the skier's gravitational potential energy using the formula:
Change in gravitational potential energy = mass * gravitational acceleration * height change
The mass of the skier is given as 75.0 kg, and the gravitational acceleration is approximately 9.8 m/s^2.
Change in gravitational potential energy = 75.0 kg * 9.8 m/s^2 * 709.831 m
Change in gravitational potential energy ≈ 523,949.869 J
The change in the skier's gravitational potential energy is approximately 523,949.869 J.