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
$v_m=5km/h$
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)
Time $=\frac{\text{relative distance}}{\text{relative speed}}$
$7.2=\frac{100}{(v+5)\left(\frac{5}{18}\right)}=12.5{\text{ms}}^{-1}$
$\Rightarrow v=45\text{km/h}$