First slide

Relative velocity in 1-d

Question

When two bodies move uniformly towards each other, the distance between them diminishes by 16 m every 10 s. If bodies move with velocities of the same magnitude and
in the same direction as before the distance between then will decrease 3 m every 5 s. The velocity of each body is.

Moderate

A

1.5 m/s, 0.8 m/s
B

1.1 m/s, 0.5 m/s
C

2.4 m/s, 1.5 m/s
D

3.0 m/s, 1.5 m/s

Solution

Let velocity of bodies be v₁ and v₂ in
first case
$u_{1} = v_{1} = v_{2} . . . . . . . (i)$
in second case
$u_{2} = v_{1} - v_{2} . . . . . . . . . (i i)$
$\begin{array}{l} ∴ v_{1} = \frac{u_{1} + u_{2}}{2} and v_{2} = \frac{u_{1} - u_{2}}{2} \\ Here u_{1} = \frac{16}{10} m / s and u_{2} = \frac{3}{5} \\ After solving we have \\ v_{1} = 1.1 m / s and v_{2} = 0.5 m / s \end{array}$

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