Final answer:
The acceleration of a skier sliding down a 15 degree slope can be calculated using the formula a = g * sin(θ). Taking the angle of the slope to be 15 degrees, the acceleration is approximately 2.53 m/s². Using the kinematic equation v = u + at, where u is the initial velocity (zero), a is the acceleration, and t is the time, we find that after 10 seconds, the skier will be moving at a speed of approximately 25.3 m/s.
Step-by-step explanation:
The acceleration of a skier sliding down a slope can be calculated using the formula:
a = g * sin(θ)
where a is the acceleration, g is the acceleration due to gravity (9.8 m/s²), and θ is the angle of the slope.
In this case, the angle of the slope is 15°. So, using the given formula, we can calculate the acceleration:
a = 9.8 * sin(15°)
a ≈ 2.53 m/s²
If we assume that the skier starts from rest, we can use the kinematic equation:
v = u + at
where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time.
Since the skier starts from rest, the initial velocity (u) is zero. We are given that the time is 10 seconds, so we can substitute these values into the equation:
v = 0 + 2.53 * 10
v ≈ 25.3 m/s
Therefore, after 10 seconds, the skier will be moving at a speed of approximately 25.3 m/s.