Question

A particle is projected in the x-y plane with y-axis along vertical. Two second after projection the velocity of the particle makes an angle 45° with the x-axis. Four second after projection, it moves horizontally. Find the velocity of projection.kindly answer this question.....

Answer 1

Projectile: Initial speed =  u , initial angle of projection: Фo.

Velocity makes an angle Ф with horizontal at time t. 

Tan Ф = dy/dx = Vy / Vx = (u SinФo - g t ) / (u CosФo)
=> Tan Ф = TanФo - (g SecФo /u) t    --- (1)

1. At t = 2 sec., Ф = 45°.
    Tan 45° = 1 = Tan Фo - (2 g Sec Фo ) /u   --- (2)
   
2. At t = 4 sec.,  Ф = 0°.
     Tan 0 = 0 = Tan Фo -  (4 g Sec Фo) / u    --- (3)
      => u = 4 g Cosec Фo      --- (4)

Substitute (4) in (2):
       Tan Фo = 2       =>            Cosec Фo = √5/2
        u = 2 √5 g