Question

A skier is accelerating down a 30.0 degree hill at 3.80 m/s2. How long (in seconds) will it take her to reach the bottom of the hill, assuming she starts from rest and accelerates uniformly, if the elevation change is 130 m?

Answer 1

To find the time it takes for the skier to reach the bottom of the hill, we can use the equations of motion. The skier is accelerating down a 30.0 degree hill at 3.80 m/s². The elevation change is 130 m. The skier will take 8.29 seconds to reach the bottom of the hill.

Step-by-step explanation:

To find the time it takes for the skier to reach the bottom of the hill, we can use the equations of motion. The skier is accelerating down a 30.0 degree hill at 3.80 m/s². The elevation change is 130 m. We can use the equation v² = u² + 2as, where v is the final velocity, u is the initial velocity, a is the acceleration, and s is the distance.

Since the skier starts from rest, the initial velocity (u) is 0. The equation becomes v² = 0 + 2(3.80)(130). Solving for v, we get v = √(2(3.80)(130)) = 31.49 m/s.

To find the time (t), we can use the equation v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time. Since the initial velocity (u) is 0, the equation becomes 31.49 = 0 + (3.80)t. Solving for t, we get t = 31.49 / 3.80 = 8.29 seconds.

Answer 2

t = 11.69s

Step-by-step explanation:

The distance traveled by the skier is given by:

`D = (H)/(sin (30))` where H=130m

D = 260m

Now, the movement down the hill is described by:

`D = Vo*t + (a*t^2)/(2)` Solving for t:

`t = \sqrt{(2D)/(a) } = 11.69s`