To find the time it takes for the skier to reach the bottom of the hill, we can use the equations of motion.
First, let's break down the given information:
- The angle of the hill is 30.0 degrees.
- The acceleration of the skier is 3.50 m/s^2.
- The initial velocity is 0 m/s (starting from rest).
- The elevation change is 120m.
We can use the following equation to find the time it takes for the skier to reach the bottom of the hill:
s = ut + (1/2)at^2
Where:
- s is the displacement or elevation change (120m in this case)
- u is the initial velocity (0 m/s)
- a is the acceleration (-3.50 m/s^2 since the skier is moving downhill)
- t is the time we want to find
Rearranging the equation, we get:
t^2 + (2u/a)t - (2s/a) = 0
Substituting the known values into the equation:
t^2 + (2 * 0/(-3.50))t - (2 * 120/(-3.50)) = 0
Simplifying further:
- (2 * 120/3.50)t + (2 * 120/3.50) = 0
- 68.57t - 68.57 = 0
Now, we solve the quadratic equation for t. Using either factoring, completing the square, or the quadratic formula, we find:
t ≈ 1.00 s
Therefore, it will take approximately 1.00 second for the skier to reach the bottom of the hill.