A police van moving on a highway with a speed of \(30~\text{km/h}\) fires a bullet at a thief’s car speeding away in the same direction with a speed of \(192~\text{km/h}\). If the muzzle speed of the bullet is \(150~\text{m/s},\) with what speed does the bullet hit the thief’s car? (Note: Obtain that speed which is relevant for damaging the thief’s car).
1. \(135~\text{m/s}\)
2. \(100~\text{m/s}\)
3. \(120~\text{m/s}\)
4. \(105~\text{m/s}\)
Speed of the police van, vp = 30 km/h = 8.33 m/s
Muzzle speed of the bullet, vb = 150 m/s
Speed of the thief’s car, vt= 192 km/h = 53.33 m/s
Since the bullet is fired from a moving van, its resultant speed can be obtained as:
= 150 + 8.33 = 158.33 m/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:
vbt = vb – vt
= 158.33 – 53.33 = 105 m/s
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