a skier is acceleration down a 30.0 degree hiss at 3.50 m/s^2. 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 120m?
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.