Rankers Physics
Topic: Kinematics
Subtopic: Distance and Displacement

A body moves 6 m north, 8 m east and 10 m vertically upwards, what is its resultant displacement from initial position?
10√2 m
10 m
10/√2 m
10×2 m

Solution:

1. Movement 1: 6 m North
\[
\text{Displacement}_1 = 6 \hat{j}
\]

2. Movement 2: 8 m East
\[
\text{Displacement}_2 = 8 \hat{i}
\]

3. Movement 3: 10 m Vertically Upwards
\[
\text{Displacement}_3 = 10 \hat{k}
\]

Total Displacement:
\[
\text{Total Displacement} = 6 \hat{j} + 8 \hat{i} + 10 \hat{k}
\]

 Magnitude of Displacement:

\[
|\text{Total Displacement}| = \sqrt{(8^2) + (6^2) + (10^2)} = \sqrt{64 + 36 + 100} = \sqrt{200} = 10\sqrt{2} \, \text{m}
\]

 

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