A car accelerating at the rate of 2 `m//s^2` from rest from origin is carrying a man at the rear end who has a gun in his hand. The car is always moving along positive x-axis. At `t=4` s, the man fires a bullet from the gun and the bullet hits a bird at `t=8`s. The bird has a position vector `40hati + 80hatj + 40hatk`. Find velocity of projection of the bullet. Take the y-axis in the horizontal plane. `(g=10m//s^2)`.

Answer

A

Explanation

Let velocity of bullet be,
`v = v_x hati+v_y hatj + v_z hat k `
At `t= 4s`, x-coordinates of car is `x_c = 1/2 at^2 = 1/2 xx 2 xx 16 = 16m.`
x-coordinate of bird is `x_b = 40 m. `
`:. x_b = x_c + v_x (8-4)`
or `40 = 16 + 4v_x`
`:. v_x = 6 m//s`
Similarly, `y_b = y_c + v_y (8-4)`
or ` 80 = 0+ 4v_y`
or `v_y = 20 m//s`
and ` z_b = z_c +v_z (8-4) -1/2 g (8-4)^2`
or ` 40 = 0+ 4v_z - 1/2 xx 10 xx 16`
or `v_z = 30 m//s`
`:.` Velocity of projection of bullet
`v = (6hat i + 20 hatj + 30 hatk) m//s` .