A skier is accelerating down a 30.0° hill at a = 2.60m/s/s.
(a) What is the vertical component of her acceleration?
(b) 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 360 m?
I get this question conceptually, but I keep getting the wrong answer. Help, please!!!
vertical? 2.60Sin30 m/s^2
height=avertical*t^2
t= sqrt (360/verticala)
Sure, I'd be happy to help you with that!
To solve this problem, we need to break down the skier's acceleration into its horizontal and vertical components.
(a) To find the vertical component of the acceleration, we need to consider the given angle of the hill. Since the hill is inclined at an angle of 30.0°, the vertical component of acceleration can be found using trigonometry.
The vertical component of acceleration can be calculated using the formula:
a_vertical = a * sin(theta)
where:
a_vertical is the vertical component of acceleration
a is the total acceleration (2.60 m/s/s in this case)
theta is the angle of inclination of the hill (30.0° in this case)
So, to find the vertical component of acceleration, we plug in the given values:
a_vertical = 2.60 m/s/s * sin(30.0°)
a_vertical = 2.60 m/s/s * 0.5
a_vertical = 1.30 m/s/s
Therefore, the vertical component of her acceleration is 1.30 m/s/s.
(b) To find the time it takes for the skier to reach the bottom of the hill, we can use the kinematic equation:
s = ut + (1/2)at^2
where:
s is the displacement (elevation change in this case, 360 m)
u is the initial velocity (0 m/s since the skier starts from rest)
a is the total acceleration (2.60 m/s/s in this case)
t is the time we want to find
Since the skier starts from rest, the initial velocity, u, is 0 m/s. Plugging in the known values, the equation becomes:
360 m = (1/2) * 2.60 m/s/s * t^2
We can rearrange the equation to solve for time, t:
t^2 = (2 * 360 m) / (2.60 m/s/s)
t^2 = 138.4615
t = sqrt(138.4615)
t ≈ 11.764 s
Therefore, it will take the skier approximately 11.764 seconds to reach the bottom of the hill.
I hope this helps! Let me know if you have any further questions.