The Exciting Adventure of a Skier on a Steep Hill

When a skier starts from the top of a hill that is 700 ft long and takes 82 seconds to reach the bottom, we can determine their final velocity at the bottom of the hill. Since the skier started from rest, their initial velocity (u) is 0.

To find the final velocity (v), we can use the equation v = u + at, where:
v = final velocity,
u = initial velocity (which is 0),
a = acceleration (due to gravity, approximately 9.8 m/s²), and
t = time taken (82 seconds).

The distance traveled by the skier can be found using the equation s = ut + 0.5at². By rearranging this equation, we can calculate the time taken using t = √(2s/a).

Given that the hill is 700 ft long, we convert this distance to meters (213.36 m). After calculating the time taken (approximately 6.68 seconds), we can find the final velocity of the skier at the bottom of the hill, which is approximately 65.17 m/s.

By understanding the equations of motion and applying them to the given data, we can determine the thrilling speed at which the skier zooms to the bottom of the hill. What an exhilarating adventure!