Question

A skier starts from rest and slides downhill. What will be the speed of the skier if he drops by 20 meters in vertical height? Ignore any air resistance (which will, in reality, be quite a lot), and any friction between the skis and the snow.

a) Depends on the angle of descent
b) √(2gh)
c) √(gh)
d) 2√(gh)

Answer 1

The speed of the skier can be determined using the equation for potential energy and kinetic energy. When the skier drops by 20 meters in vertical height, the potential energy is converted into kinetic energy. The equation for the speed of the skier is v = √(2gh), where v is the speed, g is the acceleration due to gravity, and h is the vertical height dropped.

Step-by-step explanation:

The speed of the skier can be determined using the equation for potential energy and kinetic energy. When the skier drops by 20 meters in vertical height, the potential energy is converted into kinetic energy. According to the conservation of energy, the potential energy at the top is equal to the kinetic energy at the bottom. The equation for the speed of the skier is given by:

v = √(2gh)

Where:

• v is the speed of the skier
• g is the acceleration due to gravity (approximately 9.8 m/s^2)
• h is the vertical height dropped (20 meters)

Plugging in the values, we get:

v = √(2 * 9.8 * 20) = √(392) ≈ 19.8 m/s

Therefore, the correct answer is 19.8 m/s (option c).