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?

**Details and assumptions**

- Neglect air resistance.
- The acceleration of gravity is \(-9.8~m/s^2\).
- The hill slopes down at an angle of \(\theta=30^o\) below the horizontal.
- The skier started from rest at the top of the jump.

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