# 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?

2
by niviii99

2015-05-02T11:11:51+05:30
Draw diagram according to situation
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

there is mistake in solution,OC^2=400+(30root2-30)^2
OC^2=3100-254.2,OC=root 2845.8
2015-05-04T02:52:09+05:30

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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.