Answer
Verified
396.6k+ views
Hint: Before solving the question, we must draw a diagram for better understanding. Then we will use the expression of relative velocity which is given as the difference between two velocities. We must remember to follow sign convention and we can take any of the directions as positive and the other as negative.in the case of monkeys we will add and subtract velocity of train \[A\] to make it relative velocity of monkey with suspect to train \[A\].
Formula used:
\[{{V}_{XY}}={{V}_{X}}-{{V}_{Y}}\]
Complete step by step answer:
We will try to represent the given situation in a figure.
Here, \[{{V}_{A}}\] is velocity of train \[A\], \[{{V}_{B}}\] is velocity of train \[B\] and \[{{V}_{MA}}\] is velocity of monkey with respect to the train \[A\].
Now, let us solve the questions given.
\[a)\]To find the relative velocity of train \[B\] with respect to train \[A\], we will use the relative velocity expression. Sign convention is taken as south direction as positive.
\[\begin{align}
& {{V}_{BA}}={{V}_{B}}-{{V}_{A}} \\
& {{V}_{BA}}=90-\left( -54 \right)=144km{{h}^{-1}} \\
\end{align}\]
So, the relative velocity of train \[B\] with respect to train \[A\] is found to be \[144km{{h}^{-1}}\].
\[b)\]The ground is at rest and the train \[B\] is moving with a velocity of \[90km{{h}^{-1}}\]. So the relative velocity of ground is,
\[\begin{align}
& {{V}_{GB}}={{V}_{G}}-{{V}_{B}} \\
& {{V}_{GB}}=0-\left( 90 \right)=-90km{{h}^{-1}} \\
\end{align}\]
That means the relative velocity of the ground with respect to \[B\] is, \[90km{{h}^{-1}}\] to the north direction.
\[c)\]The relative velocity of monkey with respect to a man on the ground will be,
\[{{V}_{MG}}={{V}_{M}}-{{V}_{G}}\]
Here, \[{{V}_{MG}}\] is the relative velocity of monkey w.r.t man, \[{{V}_{M}}\] is velocity of monkey and \[{{V}_{G}}\] is velocity of ground. But we don’t have velocity of monkeys. So we add and subtract velocity of train \[A\] to make the velocity of monkey as relative velocity of monkey w.r.t train\[A\].
\[\Rightarrow {{V}_{MG}}={{V}_{M}}-{{V}_{A}}+{{V}_{A}}-{{V}_{G}}\]
\[{{V}_{MG}}=\left( {{V}_{M}}-{{V}_{A}} \right)+\left( {{V}_{A}}-{{V}_{G}} \right)={{V}_{MA}}+{{V}_{AG}}\]
Where, \[{{V}_{MA}}\] is velocity of monkey with respect to the train \[A\] and \[{{V}_{AG}}\] is velocity of man w.r.t train \[A\], but the man is at rest so it will be velocity of train \[A\].
\[\Rightarrow {{V}_{MG}}=18-54=-36km{{h}^{-1}}\]
So, the velocity of the monkey w.r.t a man standing on ground will be \[36km{{h}^{-1}}\] towards north.
Note:
The soul of this solution is situated in taking the sign convention. We must not forget to include sign convention in this type of question. In sign convention we can choose any of the directions as positive but we must take the other direction as negative. Also, while finding the relative velocity of monkey w.r.t the man, we can find the velocity of monkey from the given relative velocity of monkey w.r.t the train \[A\] by taking adding the velocity of train \[A\] to the relative velocity.
Formula used:
\[{{V}_{XY}}={{V}_{X}}-{{V}_{Y}}\]
Complete step by step answer:
We will try to represent the given situation in a figure.
Here, \[{{V}_{A}}\] is velocity of train \[A\], \[{{V}_{B}}\] is velocity of train \[B\] and \[{{V}_{MA}}\] is velocity of monkey with respect to the train \[A\].
Now, let us solve the questions given.
\[a)\]To find the relative velocity of train \[B\] with respect to train \[A\], we will use the relative velocity expression. Sign convention is taken as south direction as positive.
\[\begin{align}
& {{V}_{BA}}={{V}_{B}}-{{V}_{A}} \\
& {{V}_{BA}}=90-\left( -54 \right)=144km{{h}^{-1}} \\
\end{align}\]
So, the relative velocity of train \[B\] with respect to train \[A\] is found to be \[144km{{h}^{-1}}\].
\[b)\]The ground is at rest and the train \[B\] is moving with a velocity of \[90km{{h}^{-1}}\]. So the relative velocity of ground is,
\[\begin{align}
& {{V}_{GB}}={{V}_{G}}-{{V}_{B}} \\
& {{V}_{GB}}=0-\left( 90 \right)=-90km{{h}^{-1}} \\
\end{align}\]
That means the relative velocity of the ground with respect to \[B\] is, \[90km{{h}^{-1}}\] to the north direction.
\[c)\]The relative velocity of monkey with respect to a man on the ground will be,
\[{{V}_{MG}}={{V}_{M}}-{{V}_{G}}\]
Here, \[{{V}_{MG}}\] is the relative velocity of monkey w.r.t man, \[{{V}_{M}}\] is velocity of monkey and \[{{V}_{G}}\] is velocity of ground. But we don’t have velocity of monkeys. So we add and subtract velocity of train \[A\] to make the velocity of monkey as relative velocity of monkey w.r.t train\[A\].
\[\Rightarrow {{V}_{MG}}={{V}_{M}}-{{V}_{A}}+{{V}_{A}}-{{V}_{G}}\]
\[{{V}_{MG}}=\left( {{V}_{M}}-{{V}_{A}} \right)+\left( {{V}_{A}}-{{V}_{G}} \right)={{V}_{MA}}+{{V}_{AG}}\]
Where, \[{{V}_{MA}}\] is velocity of monkey with respect to the train \[A\] and \[{{V}_{AG}}\] is velocity of man w.r.t train \[A\], but the man is at rest so it will be velocity of train \[A\].
\[\Rightarrow {{V}_{MG}}=18-54=-36km{{h}^{-1}}\]
So, the velocity of the monkey w.r.t a man standing on ground will be \[36km{{h}^{-1}}\] towards north.
Note:
The soul of this solution is situated in taking the sign convention. We must not forget to include sign convention in this type of question. In sign convention we can choose any of the directions as positive but we must take the other direction as negative. Also, while finding the relative velocity of monkey w.r.t the man, we can find the velocity of monkey from the given relative velocity of monkey w.r.t the train \[A\] by taking adding the velocity of train \[A\] to the relative velocity.
Recently Updated Pages
Assertion The resistivity of a semiconductor increases class 13 physics CBSE
The branch of science which deals with nature and natural class 10 physics CBSE
What is the stopping potential when the metal with class 12 physics JEE_Main
The momentum of a photon is 2 times 10 16gm cmsec Its class 12 physics JEE_Main
How do you arrange NH4 + BF3 H2O C2H2 in increasing class 11 chemistry CBSE
Is H mCT and q mCT the same thing If so which is more class 11 chemistry CBSE
Trending doubts
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Difference Between Plant Cell and Animal Cell
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
Change the following sentences into negative and interrogative class 10 english CBSE
Give 10 examples for herbs , shrubs , climbers , creepers
What organs are located on the left side of your body class 11 biology CBSE
Write an application to the principal requesting five class 10 english CBSE
What is the type of food and mode of feeding of the class 11 biology CBSE
Name 10 Living and Non living things class 9 biology CBSE