A particle is projected from the ground at an angle `30^@` with the horizontal with an initial speed `20 m s^-1`. After how much time will the velocity vector of projectile be perpendicular to the initial velocity ? [in second].

Explanation

You can arrive at the answer of this problem by many different ways, the degree of difficuity depends largely on the choise of reference frame. The various method given below.
Let after time t at point P the velocity v becomes perpendicular to the direction of initial velocity as shown in the figure. The horizontal of projectile remains same at all instants

` Rightarrow v sin theta = u cos theta`
The vertical component after time t.
` - v cos theta = u sin theta - "gt"`
Dividing equation (i) by (ii) we get
` - tan theta - ( u cos theta)/( u sin theta - "gt")`
` Rightarrow -u sin^(2) theta + "gt" sin theta = u cos^(2) theta " " ( " put" tan theta = (sin theta)/(cos theta))`
` Rightarrow gt sin theta = u`
` Rightarrow t = u/( g sin theta) `