Question

A train of 150 m length is going towards North at a speed of 36 km/h. A bird is flying at 18 km/h parallel to track towards South. Find the time taken by the bird to cross the train.

Answer 1

Step 1: Given that:

Length of the train($l$)= $150m$

The velocity of the train($v_t$) = $36km{h}^{-1}$ = $36\times \frac{5}{18}m{s}^{-1}$ = $10m{s}^{-1}$ (Along north direction)

The velocity of the bird($v_b$) = $18km{h}^{-1}$ = $18\times \frac{5}{18}m{s}^{-1}=5m{s}^{-1}$ (Along south direction)

Step 2: Formula used:

1. The velocity of a body with respect to other is called relative velocity.
2. If $v_1$ is the velocity of the first body and $v_2$ is the velocity of the other body then, In case both the bodies are moving in the opposite direction; the relative velocity of the first body with respect to the other will be;

$v_{12}=v_1+v_2$

3. time=$\frac{Distance}{velocity}$

Step 3: Calculation of the time taken by the bird to cross the train:

The relative velocity of the bird with respect to the train will be:

$v_{bt}=v_b+v_t$ ( As both are moving in opposite direction of each other.)

Thus, $v_{bt}=5m{s}^{-1}+10m{s}^{-1}=15m{s}^{-1}$

Now,

In order to cross the train, the bird must cross the train's total length.

Thus, the time taken by the bird = $\frac{150m}{15m{s}^{-1}}=10s$

Thus,

The time taken by the bird to cross the train is $10sec$.