Question

7. A skier slides down a hill starting with zero velocity at a height of 43 m above the bottom of the hill. The shape of the terrain is shown in Fig. 7-2. What is the velocity of the skier on top of the second, intermediate hill, whose height is 37 m? What is the skier's velocity at the bottom of the hill? Neglect all frictional effects. Is this neglect reasonable?

Answer 1

The velocity of the skier on top of the second hill is approximately 19.4 m/s, and the velocity at the bottom of the hill is approximately 29.9 m/s; neglecting friction is reasonable for this scenario.

In this scenario, the skier starts from rest at a height of 43 m and slides down the hill. To determine the skier's velocity on top of the second hill, the conservation of energy principle is applied, considering the initial potential energy at the starting height and converting it into kinetic energy on top of the second hill. The velocity is calculated to be approximately 19.4 m/s.

For the velocity at the bottom of the hill, the conservation of energy is again employed, taking into account the loss of potential energy and gain in kinetic energy. The velocity at the bottom of the hill is found to be approximately 29.9 m/s.

Neglecting frictional effects in this context is reasonable, as the question specifies to do so. Assuming an ideal scenario without friction allows for simplified calculations based on the conservation of energy, providing accurate estimations for the skier's velocities at different points along the terrain.