Question

A ski jumper launches from a ski jump that is oriented parallel to a hill. The jump has a vertical drop of 50 m and the coefficient of friction \mu between the skier and the jump is 0.05. The launch point is 5 m above the hill and there is a small lip at the bottom of the jump so that the skier launches horizontally. How long in seconds is the skier in flight?

Answer 1

Task:

A ski jumper launches from a ski jump that is oriented parallel to a hill. The jump has a vertical drop of $50\mathrm{m}$ and the coefficient of friction $\mu$ between the skier and the jump is 0.05. The launch point is $5\mathrm{m}$ above the hill and there is a small lip at the bottom of the jump so that the skier launches horizontally. How long in seconds is the skier in flight?

Solution:

$$v _ {A _ {y}} = 0$$ $$v _ {B _ {y}} = v _ {A _ {y}} - g t = - g t$$ $$y _ {B} - y _ {A} = \frac {v _ {B _ {y}} ^ {2} - v _ {A _ {y}} ^ {2}}{- 2 g} = \frac {v _ {B _ {y}} ^ {2}}{- 2 g} = - 5 m$$ $$v _ {B _ {y}} ^ {2} = 1 0 g m$$ $$v _ {B _ {y}} = - \sqrt {1 0 g m}$$ $$- \sqrt {1 0 g m} = - g t$$ $$t = \sqrt {\frac {1 0}{g} m} \approx \sqrt {\frac {1 0}{9 . 8 1 \frac {m}{s ^ {2}} m}} = \sqrt {\frac {1 0}{9 . 8 1}} s \approx 1. 0 1 9 s$$

Answer:

$$t \approx 1. 0 1 9 s$$