# A person moves 30 m north and then 20 m east and finally 30 root 2 m south west what is the displacement from the original position?

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by niviii99

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by niviii99

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A person move 30 m in north OA and then 20m in east AB and then 30√2 in south BC,then displacement is given by OC.

to find disp we have to find OC somehow

we will draw a perpendicular from O on BC

OA=BR=20

RC=30√2 -20

OR=20

By Pythagoras theorem

OC²= OR²+RC²

400+(30√2-20)²

400+(1800+400-1200√2)

√2=1.414

400+1800+400-1696.8

903.2

OC=√903.3

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See diagram.

Person starts at A, travels north to B and the moves to East till C and finally moves along CD in the SOuth West direction.

The movement in the direction CD of length 30√2 m is equal to a movement of 30 m East and then 30 meters South. This is easy to show using Pythagoras theorem.

So the displacement of the person is AD , which is 50 meters in the West direction.

Person starts at A, travels north to B and the moves to East till C and finally moves along CD in the SOuth West direction.

The movement in the direction CD of length 30√2 m is equal to a movement of 30 m East and then 30 meters South. This is easy to show using Pythagoras theorem.

So the displacement of the person is AD , which is 50 meters in the West direction.