Question

Suppose two skiers (A and B) are racing. Assume a frictionless surface! They start from the top of a mountain at the same time, and glide down to the flat area below. Just before the finish line there is a ditch. The skiers can either go down into the ditch or take a flat bridge over the ditch. Both the bridge and the ditch are covered with frictionless snow. Skier A decides to go down into the ditch. Skier B decides to go over the bridge. . Which skier gets to the finish line first, or do they arrive at the same time?

a. Skier A (ditch) arrives first
b. Skier B (bridge) arrives first
c. The skiers arrive at the same time
d. Neither skier arrives at the finish line

Answer 1

Skier A takes a route through a ditch and Skier B takes a flat bridge, both on a frictionless surface. Due to energy conservation, both skiers should arrive at the finish line simultaneously as no energy is lost in either path. So the correct option is c.

Step-by-step explanation:

The problem presented involves understanding the principles of energy conservation and physics, specifically when dealing with a frictionless environment. Both skiers start from the same height and thus have the same gravitational potential energy at the beginning of the race. As they ski down the mountain and reach the flat area, their potential energy is converted into kinetic energy. Since the surface is frictionless, no energy is lost through heat or other forms of friction.

Skier A, who decides to go down into the ditch, will follow a path where they momentarily gain additional potential energy as they go down into the ditch and then lose it again as they come up the other side. However, this does not mean they gain extra speed, as the conservation of energy ensures that they only convert this potential energy back into the kinetic energy they had before entering the ditch.

Skier B, taking the flat bridge, maintains a constant height, and thus their gravitational potential energy remains constant. All of their potential energy has already been converted into kinetic energy by the time they reach the bridge.

In the end, both skiers should arrive at the finish line at the same time, given that no additional forces are at play and energy is perfectly conserved in both cases. Therefore, the answer is c. The skiers arrive at the same time.

Answer 2

b. Skier B (bridge) arrives first

Step-by-step explanation:

This is because, skier B continues along the bring with the same velocity he started with before moving over the bridge and since the bridge is frictionless, he losses no kinetic energy and his speed is constant.

Whereas, skier A losses kinetic energy as he goes into the ditch. This is due to his change in potential energy. He thus emerges from the ditch with lesser kinetic energy than skier B and thus a slower speed.

Therefore, skier B arrives first since he moves at a constant speed.