Question

1. a snowboarder starts at the top of a 13 m icy hill. assume the snowboarder has a mass of 73 kg and a starting speed of 5.0 m/s. determine the speed at the bottom of the hill. a. 17 m/s b. 16 m/s c. 12 m/s d. 280 m/s

Explanation:

Step1: Apply conservation of mechanical energy

The total mechanical energy at the top \(E_{top}\) is the sum of kinetic energy \(K_{top}=\frac{1}{2}mv_{top}^2\) and potential energy \(U_{top} = mgh\). At the bottom \(E_{bottom}=K_{bottom}=\frac{1}{2}mv_{bottom}^2\). By conservation of energy \(E_{top}=E_{bottom}\), so \(\frac{1}{2}mv_{top}^2+mgh=\frac{1}{2}mv_{bottom}^2\).

Step2: Solve for \(v_{bottom}\)

Divide through by \(m\) (mass cancels out): \(\frac{1}{2}v_{top}^2+gh=\frac{1}{2}v_{bottom}^2\). Rearrange for \(v_{bottom}\): \(v_{bottom}=\sqrt{v_{top}^2 + 2gh}\). Substitute \(v_{top} = 5.0\space m/s\), \(g = 9.8\space m/s^2\), \(h = 13\space m\).

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Answer:

A. \(17\space m/s\)