Question

a 60 kg skier with an initial velocity of 12 m/s coasts up a hill. at the top of the hill, the skier is traveling at 9.75 m/s. assuming there is no friction in the skis, how high was the hill? (1 point) 10 m 7.35 m 0.25 m 2.5 m

Explanation:

Step1: Apply the conservation of mechanical energy

Since there is no friction, the initial kinetic energy \(K_{i}=\frac{1}{2}mv_{i}^{2}\) is converted into kinetic energy at the top \(K_{f}=\frac{1}{2}mv_{f}^{2}\) and gravitational potential energy \(U = mgh\). So, \(\frac{1}{2}mv_{i}^{2}=\frac{1}{2}mv_{f}^{2}+mgh\).

Step2: Solve for \(h\)

Cancel out \(m\) from each term: \(\frac{1}{2}v_{i}^{2}=\frac{1}{2}v_{f}^{2}+gh\). Rearrange to get \(h=\frac{v_{i}^{2}-v_{f}^{2}}{2g}\).
Substitute \(v_{i} = 12\space m/s\), \(v_{f}=9.75\space m/s\), and \(g = 9.8\space m/s^{2}\):

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Answer:

2.5 m