A plank fitted with a gun is moving on a horizontal surface with speed of `4m//s` along the positive x-axis. The z-axis is in vertically upward direction. The mass of the plank including the mass of the gun is 50 kg. When the plank reaches the origin, a shell of mass 10 kg is fired at an angle of `60^@` with the positive x-axis with a speed of `v = 20m//s` with respect to the gun in x-z plane. Find the position vector of the shell at t=2 s after firing it. Take `g = 9.8 m//s^2`.

Answer

A, B, D

Explanation

For shell `u_z = 20 sin 60^@ = 17.32 m//s`


`:. z = u_zt - 1/2 g t^2 = (17.32 xx 2) - (1/2 xx 9.8 xx 4)`
or `z = 15m rArr u_y = 0`
`:. y =0`
For `u_x` conservation of linear momentum gives,
` 50 xx 4 = (40) (v) + 10(20 cos60^@ +v)`
or `v = 2m//s`
`:. u_x = (20cos60^@)+2 = 12 m//s`
`:. x = u_xt = (12)(2) = 24m`
`:. r = (24hati + 15hatk)m` .