Question

A child of mass 30 kg skates down from the top of a ramp having a constant slope of
15 degree. The child’s speed increases from 1.5m/s to 3.0m/s as she reaches the
bottom of the ramp. A force of kinetic friction of magnitude 50 N opposes her
motion. Draw the appropriate force diagram and determine the length of the ramp.
Take g = 10m/s2

Answer 1

The diagram is below:

Write Newton's second law for the forces acting on the kid:

$$Ox:\space\space -ma=f-mg\text{ sin}\alpha,\\ \space\\ a=g\text{ sin}\alpha-\frac{f}{m}.$$

The distance can be expressed through the change of speed and the acceleration:

$$d=\frac{v_f^2-v_i^2}{2a}=\frac{m}{2}\cdot\frac{v_f^2-v_i^2}{mg\text{ sin}\alpha-f}=3.7\text{ m}.$$