Question

. A train is moving southwards at a speed of 30 ms'
A monkey is running northwards on the roof of the
train with a speed of 5 ms. What is the velocity of
the monkey as observed by a person standing on
the ground?
(a) 35 ms' in the southward direction
(b) 35 ms' in the northward direction
(c) 25 ms' in the southward direction
(d) 25 ms' in the northword direction





what would be the sign applied for the southward direction of the train ??​

Answer 1

Since the train moves southwards with a velocity of $\sf{30\ m\,s^{-1},}$ let the velocity of the train be,

$\longrightarrow\vec{\sf{v_T}}=\sf{-30\ \^j}$

where $\sf{\^j}$ represents north direction.

Here the monkey moves northwards on the roof of train with a speed of $\sf{5\ m\,s^{-1}}$ but with respect to the train.

Let this velocity of the monkey with respect to the train be,

$\longrightarrow\vec{\sf{v}}_{\sf{MT}}=\sf{5\ \^j}$

where $\vec{\sf{v_M}}$ is the velocity of monkey with respect to the ground, which has to be found out.

Since $\vec{\sf{v}}_{\sf{AB}}=\vec{\sf{v_A}}-\vec{\sf{v_B}},$

$\longrightarrow\vec{\sf{v_M}}-\vec{\sf{v_T}}=\sf{5\ \^j}$

$\longrightarrow\vec{\sf{v_M}}=\mathsf{5\ \^j}+\vec{\sf{v_T}}$

$\longrightarrow\vec{\sf{v_M}}=\mathsf{5\ \^j-30\ \^j}$

$\longrightarrow\underline{\underline{\vec{\sf{v_M}}=\mathsf{-25\ \^j}}}$

Hence the velocity of monkey as observed by a person standing on ground is $\bf{25\ m\,s^{-1}\ southwards.}$

Hence (c) is the answer.