First slide

Rectilinear Motion

Question

An aero plane moves 400m towards north, 1200m towards east and then 300m vertically upwards. Then its displacement from initial position is

Easy

A

1600m
B

1300m
C

1900m
D

1500m

Solution

Since displacement is a vector quantity the given data can be written as
$\bar{S} = 1200 \hat{i} + 400 \hat{j} + 300 \hat{k}$
$Where \hat{i}, \hat{j} & \hat{k} are the unit vectors along east, north & upward directions (or) X -axes,$
$\begin{array}{l} Y -axes and Z -axes respectively. \\ Magnitude of \bar{S} is | S | = \sqrt{(1200)^{2} + (400)^{2} + (300^{2})} \\ = 100 \sqrt{12^{2} + 4^{2} + 3^{2}} \\ = 100 \sqrt{144 + 16 + 9} \\ = 100 \sqrt{169} \\ = 1300 m \end{array}$

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