Question

After one second the velocity of projectile make an angke 45 with horizondal .after another one second it is travelling horizontally .The magnitude of initial velocity and angle of protection

Answer 1

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

Angle with horizontal at time t be Ф.

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

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

Substitute (3) in (2):
       Tan Фo = 2       =>            Cosec Фo = √5/2
        u = √5 g