question_answer

A particle is projected from a point A with a velocity V at an angle \[\theta \] (upward) with the horizontal. At a certain point B, it moves at right angle to its initial direction. It follows that:

A)  velocity of the particle at B is V

B)  velocity of the particle at B is V \[\cos \theta \]

C)  velocity of the particle at B is \[V\tan \theta \]

D)  the time of flight from A to B is \[\frac{V}{g\sin \theta }\]

Correct Answer: D

Solution :

            As,           \[\upsilon =u+at\] Considering the motion along the line AC             \[0=\upsilon -g\,\sin \theta \,t\]                 \[t=\frac{\upsilon }{g\sin \theta }\] Now consider the motion along the line C.             \[v'=0+g\cos \theta =\frac{V}{g\sin \theta }=\upsilon \cot \theta \]