First slide

Motion in a plane

Question

If A and B persons are moving with V_A and V_B velocities in opposite directions. Magnitude of relative velocity of B w.r.t. A is x and magnitude of relative velocity of A w.r.t B is y. Then

Moderate

A

x > y
B

x = y
C

x = 2y
D

2x = y

Solution

Suppose A is moving along positive x axis, so B must be moving along negative x-axis
$∴ \vec{A} = V_{A} \hat{i} and \vec{B} = V_{B} (- \hat{i})$
$∴ \vec{V_{AB}} = \vec{V_{A}} - \vec{V_{B}} = V_{A} \hat{i} - V_{B} (- \hat{i}) = (V_{A} + V_{B}) \hat{i}$
and $∴ \vec{V_{BA}} = \vec{V_{B}} - \vec{V_{A}} = - V_{B} \hat{i} - V_{A} \hat{i} = - (V_{A} + V_{B}) \hat{i}$
$|\vec{V_{AB}}| = |\vec{V_{BA}}|$
$∴ x = y$

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