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 the conservation of mechanical energy

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

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

Divide the energy - conservation equation by \(m\) (since \(m
eq0\)): \(\frac{1}{2}v_{i}^{2}+gh=\frac{1}{2}v_{f}^{2}\).
Multiply through by \(2\): \(v_{i}^{2} + 2gh=v_{f}^{2}\).
Given \(v_{i}=5.0\ m/s\), \(g = 9.8\ m/s^{2}\), and \(h = 13\ m\).
Substitute the values: \(v_{f}^{2}=(5.0)^{2}+2\times9.8\times13\).
First, calculate \((5.0)^{2}=25\), and \(2\times9.8\times13=2\times127.4 = 254.8\).
Then \(v_{f}^{2}=25 + 254.8=279.8\).
Take the square root: \(v_{f}=\sqrt{279.8}\approx16\ m/s\).

Answer:

B. \(16\ m/s\)