A professional skier reaches a speed of 58.0 m/s on a 30° ski slope.Ignoring friction,what was the minimum distance along the slope the skier would have had to travel,starting from rest?
A)172 m
B)198 m
C)343 m
D)5.92 m
E)0.291 m

Question

Quizplus · Accepted Answer

Using the equations of motion where v is final velocity, u is initial velocity, a is acceleration and s is distance travelled:

v^2 = u^2 + 2as

We are given that the initial velocity, u is 0 m/s, final velocity, v is 58.0 m/s, angle of slope, θ is 30 degrees and acceleration, a is acceleration due to gravity, g which is approximately 9.81 m/s^2.

Let's convert θ to radians:

θ = 30 degrees = π/6 radians

Now we can calculate the minimum distance, s using the above equation:

58.0^2 = 0^2 + 2(9.81)s(sin π/6)

s = (58.0^2)/(2*9.81*sin π/6) = 342.6 m ≈ 343 m (to three significant figures)

Therefore, the minimum distance along the slope the skier would have had to travel, starting from rest is 343 m. The answer is (C).

A Professional Skier Reaches a Speed of 58