A police van moving on a highway with a speed of 30km h^ –1 fires… - Vidyadip

Question

A police van moving on a highway with a speed of $30km h^{–1}$ fires a bullet at a thief’s car speeding away in the same direction with a speed of $192km h^{–1}$. If the muzzle speed of the bullet is $150m s^{–1}$, with what speed does the bullet hit the thief’s car? (Note: Obtain that speed which is relevant for damaging the thief’s car).

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Answer

Speed of the police van, $V p=30 \mathrm{~km} / \mathrm{h}=8.33 \mathrm{~m} / \mathrm{s}$ Muzzle speed of the bullet, $\mathrm{V}_{\mathrm{b}}=150 \mathrm{~m} / \mathrm{s}$ Speed of the thief's car, $\mathrm{V}_{\mathrm{t}}=192 \mathrm{~km} / \mathrm{h}=53.33 \mathrm{~m} / \mathrm{s}$ Since the bullet is fired from a moving van, its resultant speed can be obtained as: $=150$ $+8.33=158.33 \mathrm{~m} / \mathrm{s}$ Since both the vehicles are moving in the same direction, the velocity with which the bullet hits the thief's car can be obtained as: $\mathrm{V}_{\mathrm{bt}}=\mathrm{V}_{\mathrm{b}}-\mathrm{V}_{\mathrm{t}}=158.33-53.33=105 \mathrm{~m} / \mathrm{s}$

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