A police van moving on a highway with a speed of `30 km h^(-1)` fires a bullet at a thief's car speeding away in the same direction with a speed of `192 km h^(-1)`. If the muzzle speed of the bullet is `150 m s^(-1)`, with what speed does the bullet hit the thief's car?

Options

A. `120 ms^-1`
B. `90 ms^-1`
C. `125 ms^-1`
D. `105 ms^-1`

Answer

D

Explanation

(d) Velocity of police van =`30 xx (5)/(18) = (25)/(3) ms^-1`
Muzzle speed of the bullet =`150 ms^-1`
Speed of the bullet w.r.t. ground =`[150 +(25//3)] ms^-1`
Velocity of theif's car is
`192 xx (5)/(18) = (32 xx 5)/(3) = (160)/(3) ms^-1`
Relative velocity of bullet w.r.t. thief's car is
`150 + (25)/(3) - (160)/(3)`
=`150 - (135)/(3) = 105 ms^-1`.