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.