Answer to Question #96276 in Mechanics | Relativity for hugo

Question #96276
A daredevil decides to jump a canyon. It's walls are equally high and 12 m apart. He takes off by driving a motorcycle up a short ramp sloped at an angle of 19°. What minimum speed must he have in order to clear the canyon?
Expert's answer

Let us use notation @$\theta = 19^{\circ}@$, @$L = 12 m@$.

The horizontal distance, covered by the projectile aimed at an angle @$\theta@$ with initial speed @$v_0@$ is @$S = \frac{v_0^2 \sin 2 \theta}{g}@$. This distance must be minimum @$L@$ in order for a daredevil not to fall. Hence, from the previous equation, @$\frac{v_0^2 \sin 2 \theta}{g} = L \Rightarrow v_0 = \sqrt{\frac{ g L}{ \sin 2 \theta}} \approx 13.83 \frac{m}{s}@$.

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