Answer to Question #168932 in Physics for Froilan

Question

A 100−kg man is skiing across the level ground at a speed of 8.0m/s when he comes to the small slope 1.8 m higher than the ground level

(a) If the skier coasts up the hill, what is his speed when he reaches the top plateau? Assume friction between the snow and skis is negligible.

(b) What is his speed when he reaches the upper level if an 80−N frictional force acts on the skis?

Answer 1

(a) Let's use the law of conservation of energy:

$$PE_i+KE_i=PE_f+KE_f,$$ $$0+\dfrac{1}{2}mv_i^2=mgh+\dfrac{1}{2}mv_f^2,$$ $$v_f=\sqrt{v_i^2-2gh}=\sqrt{(8.0\ \dfrac{m}{s})^2-2\cdot9.8\ \dfrac{m}{s^2}\cdot1.8\ m}=5.36\ \dfrac{m}{s}.$$

(b) Let's use the law of conservation of energy:

$$PE_i+KE_i+W_{ext}=PE_f+KE_f,$$ $$\dfrac{1}{2}mv_i^2+(-F_{fr}d)=mgh+\dfrac{1}{2}mv_f^2,$$ $$v_f=\sqrt{v_i^2-2gh-\dfrac{2F_{fr}d}{m}},$$ $$v_f=\sqrt{(8.0\ \dfrac{m}{s})^2-2\cdot9.8\ \dfrac{m}{s^2}\cdot1.8\ m-\dfrac{2\cdot80\ N\cdot8\ m}{100\ kg}}=4.0\ \dfrac{m}{s}.$$