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Motion in a Straight Line

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Question : 18 of 27
Marks: +1, -0
A police van moving on a highway with a speed of 30 km h−1^{-1} fires a bullet at a thief’s car speeding away in the same direction with a speed of 192 km h−1^{-1}. If the muzzle speed of the bullet is 150 m s−1^{-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).
Solution:  
Muzzle speed of bullet, vB=150 m s−1=540 km h−1v_{B}=150\,\text{m}\,\text{s}^{-1}=540\,\text{km}\,\text{h}^{-1}
Speed of police van, vP=30 km h−1v_{P}=30\,\text{km}\,\text{h}^{-1} ,
Speed of thief car, vT=192 km h−1v_{T}=192\,\text{km}\,\text{h}^{-1}
Since the bullet is sharing the velocity of the police van, its effectivevelocity is
VB=vB+vPV_{B}=v_{B}+v_{P}
=540+30=570 km h−1=540+30=570\,\text{km}\,\text{h}^{-1}
The speed of the bullet w.r.t the thief’s car moving in the same direction
VBT=VB−vTV_{B T}=V_{B}-v_{T}
=570−192=378 km h−1=570-192=378\,\text{km}\,\text{h}^{-1}
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