A student throws a stone with velocity $v$ at an angle $\theta$ to the vertical from the surface of a lake. Air resistance can be ignored. The acceleration due to gravity is $g$.

What is the time taken for the stone to hit the surface of the lake?

A.     $\frac{{v\sin \theta }}{g}$

B.     $\frac{{v\cos \theta }}{g}$

C.     $\frac{{2v\sin \theta }}{g}$

D.     $\frac{{2v\cos \theta }}{g}$

D

Clearly when $\theta  = 90^\circ ,{\text{ }}t = 0$, so A and C must be incorrect. The relevant equation of motion relating s, v, a, t includes $\frac{1}{2}$, so D must be the correct response.