Question

A skier is gliding along at 2.0m/s on horizontal, frictionless snow. He suddenly starts down a 15∘ incline. His speed at the bottom is 12m/s .

Part A
What is the length of the incline?

Part B
How long does it take him to reach the bottom?

Answer 1

Answer on Question#39659, Physics, Mechanics

Question:

A skier is gliding along at $2.0\mathrm{m/s}$ on horizontal, frictionless snow. He suddenly starts down a $15{}^{\circ}$ incline. His speed at the bottom is $12\mathrm{m/s}$.

Part A

What is the length of the incline?

Answer:

The law of conservation of energy:

$$\frac{m v^{2}}{2} + m g h = const$$

where $h$ is height, $v$ is speed.

$$\frac{m v_{0}^{2}}{2} + m g h = \frac{m v^{\prime 2}}{2}$$

where $v_{0}$ is initial speed, $v'$ is speed at the bottom.

$$h = \frac{v^{\prime 2} - v_{0}^{2}}{2 g}$$

Distance along incline equals:

$$L = \frac{h}{\sin 15{}^{\circ}} = \frac{v^{\prime 2} - v_{0}^{2}}{2 g \sin 15{}^{\circ}} \cong 28 \, m$$

Answer: 28 m