To solve this problem, we use the equations of motion for uniformly accelerated linear motion. These equations involve the variables of initial velocity (u), final velocity (v), acceleration (a), displacement (s), and time (t). In this case, we are given the angle of the hill (30.0 degrees), the acceleration (1.80 m/s^2), and the displacement (375 m). We need to find the time it takes for the skier to reach the bottom of the hill.
First, we need to find the component of acceleration along the slope of the hill. This can be done by calculating the vertical acceleration.
The vertical acceleration (a_vertical) can be calculated using the following equation:
a_vertical = a * sin(theta)
Here, theta is the angle of the hill in radians (30.0 degrees converted to radians).
So, a_vertical = 1.80 m/s^2 * sin(30.0 degrees) = 0.90 m/s^2
Now, we can use the equation of motion for uniformly accelerated linear motion in the vertical direction to find the time it takes to reach the bottom of the hill.
The equation is:
v = u + a * t
Here, v is the final velocity (which is 0 m/s as the skier comes to rest at the bottom of the hill), u is the initial velocity (which is 0 m/s as the skier starts from rest), a is the vertical acceleration (0.90 m/s^2), and t is the time we want to find.
Plugging in the values, we have:
0 m/s = 0 m/s + 0.90 m/s^2 * t
Simplifying, we find:
0 = 0.90t
Dividing both sides by 0.90, we get:
t = 0 / 0.90 = 0
From this calculation, it seems that the skier does not take any time to reach the bottom of the hill. However, this does not make physical sense. Therefore, it appears that there may be a mistake in the given information or calculations.
Please double-check the data and calculations to ensure the accuracy of the problem.