A police van moving on a highway with a speed of 30 km/h fires a bullet at a t

Discussion Forum : Motion In One Dimension

Question -

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

Options:

A . 105 m

s^{- 1}

B . 110 m

s^{- 1}

C . 115 m

s^{- 1}

D . 120 m

s^{- 1}

Answer: Option A
:
A

The speed of the bullet with respect to ground will be,

$v_{b g}$ = $v_{b v}$ + $v_{v g}$

=150 + $\frac{25}{3}$ = $\frac{475}{3} m s^{- 1}$

Speed of thief's car is,

$v_{t g}$ =192 $\times$ $\frac{5}{18}$ = $\frac{160}{3} m s^{- 1}$

$v_{b t}$ = $v_{b g}$ - $v_{t g}$

$\frac{475}{3}$ - $\frac{160}{3}$ = 105 $m s^{- 1}$

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