Question:
A police van moving on a highway with a 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 ?
A police van moving on a highway with a 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 ?
Updated On: Jul 5, 2022
- $ 95 \,m \,s^{-1} $
- $ 105 \,m \,s^{-1} $
- $ 115 \,m \,s^{-1} $
- $ 125 \,m \,s^{-1} $
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The Correct Option is B
Solution and Explanation
Speed of police van w.r.t. ground
$ \therefore v_{PG}=30\,km\,h^{-1} $
Speed of thief?s car w.r.t. ground
$ \therefore v_{TG}=192\,km\,h^{-1} $
Speed of bullet w.r.t. police van
$ v_{BP}=150\,ms^{-1}=150\times\frac{18}{5}km\,h^{-1}=540\,km\,h^{-1} $
Speed with which the bullet will hit the thief?s car will be
$ v_{BT}=v_{BG}+v_{GT}=v_{BP}+v_{PG}+v_{GT} $
$ =540\,km\,h^{-1}+30\,km\,h^{-1}-192\,km\,h^{-1} $
$ \left(\because v_{GT}=-v_{TG}\right) $
$ =378\,km\,h^{-1}=378\times\frac{5}{18}\,ms^{-1}=105\,ms^{-1} $
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Concepts Used:
Motion in a straight line
The motion in a straight line is an object changes its position with respect to its surroundings with time, then it is called in motion. It is a change in the position of an object over time. It is nothing but linear motion.
Types of Linear Motion:
Linear motion is also known as the Rectilinear Motion which are of two types:
- Uniform linear motion with constant velocity or zero acceleration: If a body travels in a straight line by covering an equal amount of distance in an equal interval of time then it is said to have uniform motion.
- Non-Uniform linear motion with variable velocity or non-zero acceleration: Not like the uniform acceleration, the body is said to have a non-uniform motion when the velocity of a body changes by unequal amounts in equal intervals of time. The rate of change of its velocity changes at different points of time during its movement.