A skier squats low and races down a 14 �degree ski slope. During a 5 s interval, the skier accelerates at 4.2 m/s2.
What is the horizontal component of the
skier’s acceleration (perpendicular to the direction of free fall)?
To find the horizontal component of the skier's acceleration, we need to break down the given acceleration into its vertical and horizontal components.
In this case, the given acceleration (4.2 m/s^2) is in the direction of free fall, which is vertical. We want to find the horizontal component, which is perpendicular to the direction of free fall.
To determine the horizontal component, we can use trigonometry, specifically the concept of the angle of inclination of the ski slope.
The angle of inclination (theta) is given as 14 degrees. Using this angle, we can determine the horizontal component of the acceleration using the following equation:
Horizontal component of acceleration = Acceleration * cos(theta)
where cos(theta) represents the cosine of the angle of inclination.
Let's calculate the horizontal component of the skier's acceleration:
Horizontal component of acceleration = 4.2 m/s^2 * cos(14 degrees)
To find the cosine of 14 degrees, we can use a scientific calculator or an online calculator. On many scientific calculators, you can press the "cos" button followed by 14 to retrieve the cosine value. For the purpose of this explanation, let's assume the cosine value of 14 degrees is approximately 0.970.
Plugging in the values, we can calculate the horizontal component of acceleration:
Horizontal component of acceleration ≈ 4.2 m/s^2 * 0.970
Horizontal component of acceleration ≈ 4.074 m/s^2
Therefore, the horizontal component of the skier's acceleration is approximately 4.074 m/s^2.