First slide

Relative motion based problems

Question

Trains A and B are moving towards each other on the same track with velocities 40 km/hr and 20 km/hr respectively. A sparrow which can fly at 30 km/hr flies off from train A when the trains are 30 km apart. The sparrow directly moves towards the train 'B' and on reaching there flies back to 'A' and so on. Distance travelled by the sparrow till the two trains will hit, is:

Moderate

A

60 km
B

4s km
C

30 km
D

15 km

Solution

$Time of hittinng = \frac{Relative distance}{Relative velocity}$
$\frac{30 km}{(40 + 20) km / hr} = \frac{1}{2} hr$
Distance travelled by the sparrow = (30 km /hr) $(\frac{1}{2} hr)$ = 15 km

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