Starting from rest, a skier slides 100 m down a 28 ∘ slope.

How much longer does the run take if the coefficient of kinetic friction is 0.17 instead of 0?
Express your answer using two significant figures.

8.8

8.0

6.6

To calculate the time it takes for the skier to slide down the slope, we need to consider the effect of friction on the skier's motion. The equation for the time taken to slide down a slope is given by:

t = 2 * d / (g * sinθ)

Where:
t is the time taken
d is the distance traveled
g is the acceleration due to gravity (9.8 m/s^2)
θ is the angle of the slope (28∘)

First, let's calculate the time taken for the skier to slide down the slope with a coefficient of kinetic friction of 0.17:

t1 = 2 * 100 / (9.8 * sin 28∘)

Now, let's calculate the time taken for the skier to slide down the slope with a coefficient of kinetic friction of 0:

t2 = 2 * 100 / (9.8 * sin 28∘)

To find the difference in time, we subtract t2 from t1:

Δt = t1 - t2

Let's calculate the values:

t1 = 2 * 100 / (9.8 * sin 28∘) ≈ 5.1 seconds
t2 = 2 * 100 / (9.8 * sin 28∘) ≈ 5.1 seconds

Δt = t1 - t2 = 5.1 s - 5.1 s = 0 seconds

Therefore, the difference in time (Δt) is approximately 0 seconds. Thus, the run takes the same amount of time regardless of the coefficient of kinetic friction.