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A police van moving on a highway with a ...

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?

Text Solution

Verified by Experts

Speed of police van `=30xx(5)/(18)=(25)/(3)m s^(1)`
The muzzle velocity, that is, the velocity of bullet with respect to van is
`[vec v_(bullet)]_(van)=[vec v_(bullet)]_(ground)-[vec v _(van)]_(ground)`
`[vec v_(bullet)]_(ground)=[vec v _(bullet)]_(van)-[vec v _(van)]_(ground)`
`=150+(25)/(3)=(475)/(3)m s^(-1)`
Speed of thief`s car `=192xx(5)/(18)=(160)/(3)m s^(-1)`
Now velocity of bullet with respect to the thief`s car
`[vec v_(bullet)]_(can)=[vec v _(bullet)]_(ground)-[vec v _(van)]_(ground)`
`=(475)/(3)-(160)/(3)=105 m s^(-1)`
Hence the bullet hits the thief`s car with speed `105 m s^(-1)`,
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