With what acceleration does the skier descend from the slide, the angle of inclination of which to the horizon is 30 degrees?

Given:

m is the mass of the skier;

g = 9.8 meters per second squared – gravitational acceleration (constant near the surface of the earth);

u = 30 degrees – the angle of inclination of the hill to the horizon.

It is required to determine a (meter per second squared) – the acceleration of the skier.

By the condition of the problem, the friction force is not taken into account in the solution. Then, the skier descends from the slide only under the influence of the projection of gravity onto the surface of the slide. That is, according to Newton’s second law:

m * g * sin (u) = m * a;

a = g * sin (u) = 9.8 * sin (30) = 9.8 * 0.5 = 4.9 meters per second squared.

Answer: The acceleration of a skier is 4.9 meters per second squared.