Question:
Two parallel rail tracks run north-south. On one track train $ A $ moves north with a speed of $ 54 \,km \,h^{-1} $ and on the other track train $ B $ moves south with a speed of $ 90 \,km\, h^{-1} $ . what is the velocity of a monkey running on the roof of the train A against its motion with a velocity of $ 18 \,km \,h^{-1} $ with respect to the train $ A $ as observed by a man standing on the ground ?
Two parallel rail tracks run north-south. On one track train $ A $ moves north with a speed of $ 54 \,km \,h^{-1} $ and on the other track train $ B $ moves south with a speed of $ 90 \,km\, h^{-1} $ . what is the velocity of a monkey running on the roof of the train A against its motion with a velocity of $ 18 \,km \,h^{-1} $ with respect to the train $ A $ as observed by a man standing on the ground ?
Updated On: Jul 7, 2022
- $ 5\,ms^{-1} $
- $ 10\,ms^{-1} $
- $ 15\,ms^{-1} $
- $ 20\,ms^{-1} $
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The Correct Option is B
Solution and Explanation
Let the velocity of the monkey with respect to ground be $ v_{MG} $ .
Relative velocity of the monkey with respect to train $ A $ ,
$ v_{MG}=-18\,km\,h^{-1}=-18\times\frac{5}{18}\,ms^{-1}=-5\,ms^{-1} $
$ v_{MG}=v_{MA}+v_{AG}=-5\,ms^{-1}+15\,ms^{-1}=10\,ms^{-1} $
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Concepts Used:
Relative Velocity
The velocity with which one object moves with respect to another object is the relative velocity of an object with respect to another. By relative velocity, we can further understand the time rate of change in the relative position of one object with respect to another.
It is generally used to describe the motion of moving boats through water, airplanes in the wind, etc. According to the person as an observer inside the object, we can compute the velocity very easily.
The velocity of the body A – the velocity of the body B = The relative velocity of A with respect to B
V_{AB} = V_{A} – V_{B}
Where,
The relative velocity of the body A with respect to the body B = V_{AB}
The velocity of the body A = V_{A}
The velocity of body B = V_{B}