Question

A police van moving on a highway 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 thief's car)

Answer 1

Hii dear,

# Answer- 105m/s

# Given-
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

# Solution-
Resultant speed of bullet will be
vb' = vp+vb
vb' = 150 + 8.33
vb' = 158.33 m/s

Relative velocity of bullet in regard to thief's car is
vbt = vb – vt
vbt = 158.33 – 53.33
vbt = 105 m/s

Hence, bullet will hit the thief's car at the speed of 105 m/s.

Hope this is useful...

Answer 2

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Speed of the police van,

v(p) = 30 km/h = 8.33 m/s

Muzzle speed of the bullet,

v(b) = 150 m/s

Speed of the thief’s car,

v(t )= 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: v(bt) = v(b) – v(t)= 158.33 – 53.33 = 105 m/s

I hope, this will help you

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