If at point of projection , the velcoity of particle is "u" and is direction at an angle `alpha` to the horizontal , then show that it will be moving at right angles to the its initial direction after a time `((u "cosec" alpha))/(g)`

Explanation

Let "t" be the time after which velocity beomes perpendicular to its initial direction . As u and v are perpendicular , the angle between v and vertical will be `alpha`
Initial velcoity .u. `= (u cose alpha hat(i) + u sin alpha hat(j))`
After t sec , velocity .v. ` = { u cos alpha hat(i) + ( u sin alpha - "gt")hat(j)}`
`because` these are perpendicular their dot product is zero .
` therefore ( u cos alpha + u sin j).{u cos alpha i + (u sin alpha - "gt")j} =0` and `t = ( u cosec alpha)/(g)`