Question

a train of length 120m travels at a speed of 57km/h. in what time it will pass a man who is walking at 3km/h in the opposite direction? (hint: Vab= Va+ Vb, relative velocity A w.r.t.B)

Answer 1

it is a question of relative velocity.... hope you find the solution useful

Answer 2

The time required by the train for passing through the man is 7.2 seconds.

Given:

Length of the train=120m

Speed of the train=57km/hr

Solution:

Convert the speed into m/s

$=57 \times \frac{5}{18}$

$=\frac{95}{6} m/s$

Velocity of the man$=3 \times \frac{5}{18}$

$=\frac{5}{6} m/s$

Man walks at 3km/h in the opposite direction to the train

We have to find the time taken by the man

The required time $=\frac{d i s t a n c e}{r e l a t i v e\ v e l o c i t y}$

$=\frac{120}{\frac{95}{6}-\left(-\frac{5}{6}\right)}$

By taking LCM let us simplify  

$=\frac{120}{\frac{100}{6}}$

$=120 \times \frac{6}{100}$

$=\frac{36}{5}$

=7.2s  

Hence the time required by the man who is walking at 3km required is 7.2 seconds.