Question

A $100\text{m}$ long train crosses a man travelling at $5\text{km/h}$ in opposite direction in $7.2\text{s}$. Then the velocity of the train is

• A. $40\text{km/h}$
• B. $25\text{km/h}$
• C. $20\text{km/h}$
• D. $45\text{km/h}$

Answer 1

The correct option is D $45\text{km/h}$

Let $v_T$ be the velocity of the train and $v_M$ be the velocity of man.
According to question
$v_m=5\text{km/h}$
Now, velocity of train w.r.t man is given by
$v_{TM}=v_T-v_m=v_T-(-5)$
$=v_T+5$ ($\because$ man is travelling in opposite direction to that of the train)
Relative distance between both man and the train $=100\text{m}=0.1\text{km}$
$\text{Time}=\frac{\text{relative distance}}{\text{relative speed}}$
$\frac{7.2}{60\times 60}=\frac{0.1}{(v_T+5)}$
$\Rightarrow v_T=45\text{km/h}$