First slide

Relative velocity in 1-d

Question

A bird flies to and fro between two cars which move with velocities v₁=20 m/s and v₂=30 m/s. If the speed of the bird is v₃=10 m/s and the initial distance of separation
between them is d=2 km, find the total distance covered by the bird till the cars meet.

Moderate

A

2000 m
B

1000 m
C

400 m
D

200 m

Solution

$Time to meet the cars: t = \frac{d}{v_{1} + v_{2}}$
Distance travelled by bird in this time
$s = v_{3} t = \frac{v_{3} d}{v_{1} + v_{2}} = \frac{10 \times 2000}{(20 + 30)} = 400 m$

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