Question

question 3
a 75.0 kg skier rides a 2,830 m long lift to the top of a mountain. the lift makes an angle of 14.6° with the horizontal. what is the change in the skiers gravitational potential energy?

5.24×10⁵j
2.01×10⁶j
2.08×10⁶j
1.67×10⁵j

Explanation:

Step1: Find the height \( h \)

Using the formula \( h = L\sin\theta \) (where \( L = 2830\ m \) is the length of the lift and \( \theta=14.6^{\circ} \)), we have \( h = 2830\times\sin(14.6^{\circ}) \).

$$h = 2830\times0.2524\approx714.2\ m$$

Step2: Calculate gravitational potential energy \( \Delta U \)

The formula for gravitational potential energy is \( \Delta U=mgh \) (where \( m = 75.0\ kg \), \( g = 9.8\ m/s^{2} \), and \( h\approx714.2\ m \)).

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Answer:

\(5.24\times 10^{5}\ J\) (First option)