Question

A skier starts from rest at the top of a 42 m hill, skis down a 39° incline into a valley, and continues up a 36 m high hill. Both hill heights are measured from the valley floor. Assume that you can neglect friction and the effect of ski poles.
1. How fast is the skier moving at the bottom of the valley?
2. What is the skier’s speed at the top of the next hill?
3. Does (a) or (b) depend on the angles of the hills?
A. Does the part (b) depends on the angle.
B. Does neither depends on the angle.
C. Does the part (a) depends on the angle

Answer 1

Answer:

1. The speed of the skier at the bottom of the valley is 28.706 m/s

2. The skier's speed at the top of the next hill is 10.85 m/s

3. The correct option is;

B Does Neither depends on the angle

Explanation:

Here we have conversion of mechanical energy from kinetic to potential energy as follows;

1. At the top of the 42 m hill, the potential energy of the skier is

P.E. = m·g·h = m × 9.81 × 42 = 412.02·m J

The Kinetic energy of the skier at the bottom of the hill is

1/2·m·v² = 412.02·m J

Since the mass is constant, we have'

v² = 824.04  and

v = √824.04 = 28.706 m/s

The speed of the skier at the bottom of the valley = 28.706 m/s

2. The speed at the top of the next hill is given by;

1/2·m·v² = m·g·(h₁-h₂)

v² = 2·g·(h₁-h₂) = 2×9.81×6 = 117.72

v = 10.85 m/s

The skier's speed at the top of the next hill = 10.85 m/s

3. Neither the solution of part (a) nor the solution of part (b) depend on the angle.

The correct option here is;

B Neither depends on the angle.