Question

a particle is projected at an angle θ with horizontal. its velocity of projection is u

Answer 1

the velocity of projection of the object be u with angle of projection θ with the horizontal direction. The vertical component of the velocity of projection is

usin θ and the horizontal component is ucosθ.Now if t be the time after the projection of the projectile, its direction of velocity makes angle $\alpha$ with the horizontal.Let the velocity of the projectile after t sec be v

The vertical component of the velocity after time t will be vsin $\alpha$

But the horizontal component remains unaltered as ucosθ

So v cos $\alpha$= u cos θ ⇒ v = 1 cos $\alpha$× u cos θ = u cos θ sec $\alpha$