Physics Problem: slopes and angles

Question

A skier goes down a slope with an acceleration of 4.1 m/s^2. If we ignore friction and air resistance, wat is the angle of the slope with respect to the horizontal direction?

Answer 1

On a slope, there are two components of gravitational acceleration (g = 9.8 m/s²).

The component parallel to the slope, given by a_x = g sin(θ), determines acceleration down the slope.

The component perpendicular to the slope, given by a_y = g cos(θ), determines normal force (which we're not interested in here).

Since we know acceleration down the slope, we can solve for the angle of the slope (θ) as follows:

a_x = g sin(θ) means that sin(θ) = a_x/g

Taking the inverse sine of both sides gives

θ = sin^–1(a_x/g)

Plugging in a_x = 4.1 m/s² and g = 9.8 m/s² gives

θ = sin^–1(4.1/9.8) = 24.7°

Answer (if we're required to round to 2 significant figures)

The angle of the slope with respect to the horizontal direction is 25°