Question:

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

Updated On: Nov 2, 2023
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Solution and Explanation

Speed of the police van, \(\text v_p\) = 30 \(\text{km}/\text h\) = 8.33 \(\text{m}/\text s\)
Muzzle speed of the bullet, \(\text v_b\) = 150 \(\text{m}/\text s\)
Speed of the thief’s car, \(\text v_t\)= 192 \(\text{km}/\text h\) = 53.33 \(\text{m}/\text s\)
Since the bullet is fired from a moving van, its resultant speed can be obtained as: 
= 150 + 8.33 = 158.33 \(\text{m}/\text s\)
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: 
\(\text v_{bt}\)\(\text v_b-\text v_t\) = 158.33 – 53.33 = 105 \(\text{m}/\text s\)

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