A skier squats low and races down an 11◦ ski slope. During a 3 s interval, the skier accelerates at 2.7 m/s^2 . What is the horizontal component of the skier’s acceleration (perpendicular to the direction of free fall)? Answer in units of m/s^2.
well, I'd say it's 2.7 cos 11°
When you're not given much info, the formulas involved must be relatively simple. Naturally, if the ramp were horizontal (0°), all the acceleration would be horizontal.
To find the horizontal component of the skier's acceleration, we need to consider the given information about the slope angle and the skier's overall acceleration.
First, let's break down the skier's acceleration into its vertical and horizontal components. The vertical component is related to the skier's acceleration due to gravity, which is approximately 9.8 m/s^2 (assuming no air resistance). The horizontal component is perpendicular to the direction of free fall and is caused by the skier's own actions.
Since the slope angle is 11 degrees, we can use trigonometry to find the horizontal component of acceleration. The horizontal component can be calculated using the formula:
Horizontal Component of Acceleration = Acceleration x cos(theta)
where theta is the angle of the slope (11 degrees) and cos(theta) is the cosine of the angle.
Plugging in the values:
Horizontal Component of Acceleration = 2.7 m/s^2 x cos(11 degrees)
To calculate this, convert the angle from degrees to radians: 11 degrees = 0.19 radians.
Now, use a calculator to find the cosine of 0.19 radians: cos(0.19) ≈ 0.983.
Finally, multiply the skier's overall acceleration by the cosine of the slope angle:
Horizontal Component of Acceleration ≈ 2.7 m/s^2 x 0.983 ≈ 2.654 m/s^2.
Therefore, the horizontal component of the skier's acceleration is approximately 2.654 m/s^2.