A professional skier reaches a speed of 39.6 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?Select one:a.640 mb.160 mc.320 md.110 m
Question
A professional skier reaches a speed of 39.6 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?Select one:a.640 mb.160 mc.320 md.110 m
Solution
To solve this problem, we can use the formula for the final velocity of an object moving with constant acceleration:
v^2 = u^2 + 2as
where: v = final velocity = 39.6 m/s u = initial velocity = 0 (since the skier starts from rest) a = acceleration = g * sin(θ) (since the skier is moving down a slope, the acceleration is the component of gravity in the direction of motion) s = distance traveled along the slope
We want to solve for s, so we rearrange the formula to get:
s = (v^2 - u^2) / (2a)
Substituting the given values:
s = (39.6 m/s)^2 / (2 * 9.8 m/s^2 * sin(30°)) s = 1568.16 m^2/s^2 / (19.6 m/s^2) s = 80 m
So, the minimum distance along the slope the skier would have had to travel, starting from rest, is 80 m. Therefore, the correct answer is b. 80 m.
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