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Question

A person moves 30m north and then 20m east and then 302msouthwest. His displacement from the origin position will be?


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Solution

Step 1: Given data

First, the person moves in the north direction for 30m

Then, the person moves in the east direction for 20m

Then, the person moves in the southeast direction for 302m

Step 2: Formula used

Displacement is the change in positions and can be written as OC=OA+AB+BC

Step 3: Solution

First, the person moves toward 30mnorth.

OA=0i^+30j^+0k^

Now, the person moves toward 20meast.

AB=20i^+0j^+0k^

Now, the person moving toward 302mthe southwest

BC=-302cos45°i^+-302sin45°j^+0k^BC=-30i^-30j^+0k^

[Here, the horizontal component of 302msouthwest =-302cos45°, the vertical component of 302msouthwest =-302sin45° ]

Now, displacement OC is

OC=OA+AB+BC=-10i^

[Here, displacement is found by vector sum because it is a vector quantity]

Hence, the displacement is of magnitude 10m in the west direction.


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