A person moves 30 metre north, then 20 metre
east, then 30v2 metre south-west. His displace-
ment from the original position is
(1) 14 metre south-west
.(2) 28 metre south
(3) 10 metre west
(4) 15 metre east
Answers
Answer:
The person, let us assume has started at the origin (0,0) of X-axis ( initial position) .
He moved in the north by 30 m(first movement). That amounts to moving in the OY -direction .
He then moved 20 m in the East( second movement) . That amounts to moving in the OX- direction.
Or, in other words he moved away from the origin (0,0) and is at (20,30) co-ordinate (after second movement) .
This amounts to saying that he is at a linear distance of d = √30^2+20^2 =36.055 m from the origin (0,0) in the N-E direction.
He has now moved from this point (20,30) towards the S-W direction, on his third leg of his journey.
Or, in other words he is moving in a diametrically opposite direction from his (20,30) point towards the origin (0,0).
The directions N-E & S-W are the two diametrically opposite directions.
He has on his last leg of journey ( third movement) has moved 30√2 m in the S-W direction.
This amounts to moving 30√2=30×1.414=42.426 m in the S-W direction.
As he is at the point (20,30) ( second position) and moved 42.426 m in the S-W direction, he is deemed to have passed through the origin (0,0) and assumed to have gone ahead in the S-W direction.
As he was originally at(20,30) on the last leg of his journey & moved 30√2= 42.426 m in S-W direction, he is deemed to have passed through (0,0) and went ahead by(42.426 -36.055) m = 6.371 m from the origin (0,0) in the S-W direction.
Or, in other words he has been displaced by 6.371 m from his initial position (0,0) in the S-W direction.