First slide

Relative velocity in 1-d

Question

A police van moving on a high way with a speed of 30km/h fires a bullet at a thief’s car speeding away in the same direction with a speed of 192km/h. If the speed of the bullet with respect to police Van is 150m/s, with what relative speed does the bullet hit the thief’s car?

Moderate

A

90 m/s
B

105 m/s
C

110 m/s
D

120 m/s

Solution

1. The speed of the bullet with respect to police
$v_{B P} = 150 m / s,$
Speed of police van
$\begin{array}{l} v_{P} = 30 km / h = 30 \times \frac{5}{18} m / s = 8.3 m / s \\ \Rightarrow v_{B P} = v_{B} - v_{P} \\ v_{B} = v_{B P} + v_{P} = (150 m / s + 8.3 m / s) = 158.3 m / s . \\ v_{T} = 192 km / h = 192 \times \frac{5}{18} m / s = 53.3 m / s \\ \Rightarrow v_{B T} = v_{B} - v_{T} = (158.3 - 53.3) m / s = 105 m / s \end{array}$
Therefore, the correct answer is (B).

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