A ball is projected with initial speed u at an angle theta above the horizontal . Calculate the time afterwhich ball will be moving at right angle to its initial velocity.

A ball is projected with initial speed u at an angle theta above the h

1.	A ball is projected with initial speed u at an angle theta above the horizontal . Calculate the time afterwhich ball will be moving at right angle to its initial velocity.
Answer» Solution :Let particle be projected from the point A and its velocitybecome perpendicular to its initialvelocityat pointBasshown in thefigure. Let velocity ofthe ball at point B be v . Refer to thefigure to understand that velocity at point B will make an ANGLE ` theta`with the vertical. Components of VELOCITIES are shown in figure . We know that horizontal component of velocity remains constant, hence we can write the following: `v sin theta =u costheta` `rArr v=(u cos theta)/(sin theta)` Let US asume upward direction as positivedirection and apply equation of kinematics . `v_(y)=u_(y)+a_(y)t` `rArr (-v cos theta)=(u sin theta)+ (-g) t` SUBSTITUTING VALUE of v from equation(i), we get thefollowing: `"gt"=u sin theta+(u cos theta)/( sin theta) cos theta` `t=(u)/(g) cosec theta`