Question

a body is projected at V* . find velocity of body when it covers equal distance in horizontal and vertical directions.

Answer 1

Given that a projectile is projected with an initial velocity of u , at an angle Ф with the horizontal.

Speeds:       Vy = u SinФ - g t           and    Vx = u CosФ 
Distances:   Sy = u SinФ t - 1/2 g t²          Sx = u CosФ t

Given Sy = Sx 
=>   t = 0 or,     t = 2u/g (SinФ - CosФ)

So    Vy at time t :  Vy = u SinФ - 2u (sinФ - cosФ)
                                    = u (2 CosФ - sinФ)
        Vx at time t :   Vx = u cosФ

So velocity (magnitude ) at time t :
          V = u √[3+ 2 Cos2Ф - 2 Sin2Ф ]      on simplification.

Distance covered = S = u²/g * [Sin2Ф - Cos2Ф - 1]