Question

A ski that is placed on snow will stick to the snow. However, when the ski is moved along the snow, the rubbing warms and partially melts the snow, reducing the coefficient of friction and promoting sliding. Waxing the ski makes it water repellent and reduces friction with the resulting layer of water. A magazine reports that a new type of plastic ski is especially water repellent and that, on a gentle 175 m slope in the Alps, a skier reduced his top-to-bottom time from 69 s with standard skis to 40 s with the new skis. (a) Determine the magnitude of his average acceleration with each pair of skis.

Answer 1

accleraion normal ski 0.0735 m/s², new ski 0.219 m/s²

Step-by-step explanation:

This exercise should work with the one-dimensional kinetic equations, specifically with the equation

x = v₀ t + ½ a t²

When the skier is at the exit they are at rest, so their initial speed is zero

(v₀ = 0)

x = ½ a t²

Let's calculate the acceleration for normal skiing

a₁ = 2 x / t²

a₁ = 2 175/69²

a₁ = 0.0735 m/s²

a₁ = 7.35 10⁻² m/s²

Let's calculate the acceleration with the new plastic ski

a₂ = 2 x / t₂²

a₂ = 2 175/40²

a₂ = 0.219 m/s²

a₂= 2.19 10⁻¹ m/s²