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A police van moving with a speed of 36 km/h fires a bullet at a thief’s car speeding away in the same direction with a speed of 180 km /h . If the muzzle speed of bullet is 150 m/s , what is the time taken by the bullet to hit the thief’s car, if the distance between the two vehicles is 1km at the instant the bullet is fired.

A police van moving with a speed of 36 km/h fires a bullet at a thief’s  car  speeding away in the same direction with a speed of 180 km /h  . If the muzzle speed of bullet is 150 m/s , what is the time taken by the bullet to hit the thief’s car, if the distance between the two vehicles is 1km at the instant the bullet is fired.

Grade:12th pass

1 Answers

Vikas TU
14149 Points
7 years ago
First Find the relative velocity of bullet w.r.t van.
.i.e. => 150 – 10 = 140 m/s.
 
vel. of theif's car is: 180000/3600 = 1800/36 = 200/4 = 50 m/s.
 
Now let x be the distance travelled by car at which the theif would be caught .
 
Therfore,
For theif's car eqns of motion :
x = 50*t …....................................(1)
Time would be same of course in order to hit the car.
 
For bullet eqn. od motion:
(x+1000) = 140*t.............................(2)
solving eqns. (1) and (2)
50t + 1000 = 140t
90t = 1000
t = 100/9 = 11.11 seconds (approx.)

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