The distance a bird flies

Classical Mechanics Level 2

Two trains, each having a speed of $30 \text{ km/h},$ are headed at each other on the same straight track. A bird that can fly $60 \text{ km/h}$ flies off the front of one train when they are $60 \text{ km}$ apart and heads directly for the other train. On reaching the other train, the bird flies directly back to the first train, and so forth. What is the total distance the bird travels before the two trains collide?

80 km 50 km 60 km 40 km

2 solutions

Aditya Kottapalli
Apr 30, 2014

it takes exactly one hour for the trains separated 60 km and moving opposite to each other at 30 kmph, velocity of bird was give as 60 kmph so it covers 60 km in an hour

Jung Hyun Ran
May 20, 2014

The equations of motion:

One of trains: $x_1= V_1\times t_1$
The other train: $x_2= V_2\times t_2$

When the trains collide, $t_1=t_2=t$ ,And we get: $x_1+x_2=60 \Leftrightarrow t\times \left( V_1+V_2 \right)=60$ $\Rightarrow$ $t= \frac{60}{V_1+V_2}$ $= \frac{60}{30+30} =1 \quad \left( h \right)$

And, the time travel of the bird $=$ the time travel of the trains. So, the total distance the bird travels: $S=V_3\times t = 60\times 1 = 60 \left( km \right)$

The distance a bird flies

2 solutions

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