At what speed would he arrive at the lower peak?

Question

Two snow covered peaks are at elevations of 862 m and 741 m above the valley between them. If a skier starts from rest on the higher peak and just coasted down without exerting any effort, at what speed would he arrive at the lower peak?

Answer 1

To solve this problem, we can use the conservation of mechanical energy. At the top of the higher peak, the skier has only potential energy, which is converted into kinetic energy as the skier slides down the slope.

At the bottom of the lower peak, all of the potential energy has been converted into kinetic energy. Therefore, we can equate the potential energy at the higher peak to the kinetic energy at the lower peak:

mgh1 = (1/2)mv^2

where m is the mass of the skier, g is the acceleration due to gravity (9.81 m/s^2), h1 is the height of the higher peak (862 m), v is the speed of the skier at the bottom of the lower peak, and we have assumed that there is no air resistance.

When we simplify the equation , we have

v = √(2gh1)

Substituting the given values, we get:

v = √(2 x 9.81 m/s^2 x 862 m) v ≈ 120.9 m/s

Therefore, the skier would arrive at the lower peak with a speed of approximately 120.9 m/s.

Answer 2

mg(h₁ - h₂) = mv₂²/2 (v₁ = 0); So, v₂ = √2g(h₁ - h₂) = √2·9.8m/s²(862m - 741m) = 48.7 m/s