A body is thrown from the surface of the Earth at an angle $\alpha$ to the horizontal. If the maximu

Question

A body is thrown from the surface of the Earth at an angle $\alpha$ to the horizontal. If the maximum height of ascent is exactly equal to the horizontal range, find the value of $	an \alpha$.

Professor PC Thomas Classes · Answer

Maximum height $H = \frac{v_0^2 \sin^2 \alpha}{2g}$. Horizontal range $R = \frac{v_0^2 \sin 2\alpha}{g} = \frac{2v_0^2 \sin \alpha \cos \alpha}{g}$. Equating $H = R$ gives $\frac{\sin^2 \alpha}{2} = 2 \sin \alpha \cos \alpha$. Since $\sin \alpha 
eq 0$, we get $	an \alpha = 4$.