question_answer

A particle is projected from point \[O\] with velocity \[u\] in a direction making an angle \[\alpha \] with the horizontal. At any instant its position is at point \[p\] at right angles to the initial direction of projection, Its velocity at point \[p\] is

A) \[u\tan \alpha \]            

B) \[u\cot \alpha \]

C) \[u\operatorname{cosec}\alpha \]

D) \[u\sec \alpha \]

Correct Answer: B

Solution :

[b] Horizontal velocity at point '[O'=u cos\[\alpha \]Horizontal velocity at point 'P'=v sin \[\alpha \] In projectile motion horizontal component of velocity remains constant throughout the motion \[\therefore v\sin \alpha =u\cos \alpha \] \[\Rightarrow v=u\cot \alpha \]