Question

A train of $150m$ length is going toward the north direction at a speed of $10 m/s$. A parrot flies at a speed of $5 m/s$ towards the south direction parallel to the railway track. The time taken by the parrot to cross the train is equal to
(A). $12s$
(B). $8s$
(C). $15s$
(D). $10s$

Answer 1

Hint- When there are two moving bodies in two different frames then the concept of the relative velocity comes into picture. Relative velocity of any two-moving body (let A and B) is the velocity of body A when it is observed by an observer on the body B and vice-versa. When two moving object move in the same direction then the relative velocity of one object with respect to other will be the difference in the velocity of two moving objects and if the object is moving in the opposite direction then the relative velocity of one object with respect to other will be the addition of the velocities of two of them.

Complete step-by-step answer:
Given,
Length of the train =${l_t} = 150 m$
Velocity of the train= $10 m/s$ in the north direction
Velocity of the parrot=${v_P} = 5 m/s$ in the south direction
Here we see that the train is moving in the north direction and the flying parrot is moving in the south direction. So, they are moving in the opposite directions.
So, to get the relative velocity of parrot with respect to the train we will add the velocities of the train and parrot.
So let the relative velocity of parrot with respect to the train = ${v_{PT}}$
Now, ${v_{PT}} = 10 m/s + 5 m/s = 15 m/s$
Now the time taken by the parrot to cross the train$= t$=length of the train divided by the relative velocity of the parrot.
So $t = \dfrac{{{l_T}}}{{{v_{PT}}}}$
$\Rightarrow t = \dfrac{{150}}{{15}} = 10s$
$t = 10s.$
Hence the time taken by the parrot to cross the train is $10s$.
So option (D) is the correct option.

Note- General formula for the relative velocity is ${v_r} = {v_1} - {v_2}$, where we choose the positive or negative sign of ${v_2}$according to the direction of the ${2^{nd}}$ object with respect to the ${1^{st}}$ object. If the direction of ${2^{nd}}$object is same as that of the ${1^{st}}$object then the sign of the velocity of the ${2^{nd}}$object will be positive and if it is opposite then the sign will be negative.
Hence the relative velocity of the objects moving in same direction,
${v_r} = {v_1} - {v_2}$
And the relative velocity of the objects moving in opposite direction,
${v_r} = {v_1} - ( - {v_2})$
$\Rightarrow {v_r} = {v_1} + {v_2}$.