3. a snowboarder starts at the top of a 13 m icy hill. assume the snowboarder has a mass of 73 kg and a…

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\neq0)): (\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)