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Question
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? (Note: Obtain that speed which is relevant for damaging the thief’s car).
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Solution
Speed of the police van, vp = 30 km/h = `(30xx100)/3600` = 8.33 m/s
Muzzle speed of the bullet, vb = 150 m/s
Speed of the thief’s car, vt = 192 km/h = `(192xx1000)/3600` = 53.33 m/s
Bullet's speed relative to ground (from police van) = vb + vp
= 150 + 8.33 = 158.33 m/s
Since both vehicles are moving in the same direction, the velocity with which the bullet hits the thief’s car can be obtained as follows:
vbt = vb + vp - vt
= 158.33 - 53.33 = 105 m/s
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