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# What is the velocity of a monkey running on the roof of the train A (moving with velocity $54{\text{ km/hour}}$) against its motion with a velocity of $18{\text{ km/hour}}$ with respect to the train A as observed by a man standing on the ground? A) $5\;{\text{m/s}}$B) $10{\text{ m/s}}$C) $15{\text{ m/s}}$ D) $20{\text{ m/s}}$

Last updated date: 18th Jun 2024
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Hint: When the velocity of a moving body is observed from a frame of reference which is also in motion then the measured value of the velocity is called the relative velocity. When the velocity of a moving body is observed from a frame of reference which is stationary then the measured value of the velocity is called the absolute velocity of the body.

Complete step by step solution:
When a body A is moving with a velocity $\overrightarrow {{v_A}}$ and another body is moving with velocity $\overrightarrow {{v_B}}$, then the relative velocity of body A when observed by body B, it is called the relative velocity of body A with respect to body B.
The relative velocity of body A with relative to body B can be given as,
$\overrightarrow {{v_{AB}}} = \overrightarrow {{v_A}} - \overrightarrow {{v_B}}$
Let the direction of the motion of train A be positive, then the direction opposite to the direction of motion of train A will be negative.
Velocity of train A, $\overrightarrow {{v_A}} = 54{\text{ km/h}}$
Velocity of monkey with relative to the man standing on the ground is the absolute velocity of the monkey, $\overrightarrow {{v_{MA}}} = - 18{\text{ km/h}}$
The velocity of the monkey observed by a man standing on ground is the absolute velocity of the monkey.
Let the absolute velocity of the monkey is $\overrightarrow {{v_M}}$
Using relative velocity formula,
$\overrightarrow {{v_{MA}}} = \overrightarrow {{v_M}} - \overrightarrow {{v_A}}$
Putting the value of velocities in the relative velocity equation, we get
$- 18{\text{ km/h}} = \overrightarrow {{v_A}} - 54{\text{ km/h}} \\ \overrightarrow {{v_M}} = \left( {54 - 18} \right){\text{ km/h}} \\ {\text{ = 36 km/h}} \\$
Hence, the absolute velocity of monkey is $36\;{\text{km/h}}$
As we know,
$1{\text{ km}} = 1000{\text{ m}} \\ {\text{1 hour}} = 3600{\text{ s}} \\$
Then, the absolute velocity of monkey becomes,
$\overrightarrow {{v_A}} = \left( {36 \times \dfrac{{1000}}{{3600}}} \right){\text{ m/s}} \\ = 10{\text{ m/s}} \\$
So, the velocity of the monkey is $10{\text{ m/s}}$

Hence, option B is the correct answer.

Note: The velocity of the monkey on the roof is the velocity of the monkey relative to the train.
When the velocity of a monkey is observed by the man on the ground then the observed velocity is the absolute velocity of the monkey.