A skier is accelerating down a 30.0 degrees hill at 1.80m/s^2.

How long will it take her to reach the bottom of the hill, assuming she starts from rest and accelerates uniformly, if the elevation change is 375 m?

Apparently the answer isn't 20.4 s...
Can someone help me please?

The distance traveled to reach the bottom is 375/sin30 = 750 m

To travel Z = 750 m while accelerating uniformly in that direction at a = 1.80 m/s^2, the time T needs to satisfy the equation

(a/2)*T^2 = 750
T^2 = 750/0.9
T = 28.9 s

To get 20.4 s, you confused the elevation change with the distance traveled.

Well, it seems like this skier is really eager to hit the slopes... or maybe just in a hurry! Let me help you out with some clowny calculations.

First, let's break down this downhill journey. We're given that the skier is accelerating down a 30.0 degree hill at 1.80 m/s^2. So, that's our acceleration (a).

We also know that the skier starts from rest, which means her initial velocity (v0) is 0 m/s. We're given the elevation change (h) of 375 m, which is our displacement (d).

Now, we can try using the equation of motion:

d = v0 * t + 0.5 * a * t^2

Since the skier starts from rest, v0 can be ignored, and the equation simplifies to:

d = 0.5 * a * t^2

Plugging in the values we have:

375 = 0.5 * 1.80 * t^2

Solving for t, we get:

t^2 = 375 / (0.5 * 1.80)
t^2 = 416.67
t ≈ 20.42 s

Ah, there you go! It looks like the answer is approximately 20.42 seconds, not 20.4 s. So, it seems like someone was just rounding a little too soon. Remember, clowning around with numbers can lead to some unexpected results. Stay safe on the slopes and have a jolly good time!

To find the time it takes for the skier to reach the bottom of the hill, we can use the equations of motion.

First, we need to resolve the acceleration into its components parallel and perpendicular to the slope.

The parallel component of acceleration is given by:
a_parallel = a * sin(theta)
where a is the total acceleration (1.80 m/s^2) and theta is the angle of the hill (30.0 degrees).

a_parallel = 1.80 m/s^2 * sin(30.0 degrees)
a_parallel ≈ 0.90 m/s^2

Next, we need to calculate the time it takes for the skier to travel the vertical distance, which is equal to the elevation change of 375 m.

Using the equation of motion:
s = ut + (1/2)at^2

Since the initial velocity (u) is zero, the equation simplifies to:
s = (1/2)at^2

Plugging in the values:
375 m = (1/2) * 0.90 m/s^2 * t^2

Multiplying both sides by 2 and dividing by 0.90 m/s^2:
t^2 = (2 * 375 m) / 0.90 m/s^2
t^2 ≈ 833.33
t ≈ √833.33
t ≈ 28.87 s

Therefore, it will take the skier approximately 28.87 seconds to reach the bottom of the hill, not 20.4 seconds.

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.