A particle moves 4√2 m in South-West direction, 12 m in upward direction and then 1 m in East direction. Find the net displacement.
A) 13 m
B) 17 m
C) 14 m
D) 18 m
Answer (2)
The net displacement of the particle is calculated to be 13 m by breaking down its movements into components and applying the Pythagorean theorem. Therefore, the correct option is A) 13 m.
;
To find the net displacement of the particle, we need to consider the movement in each direction separately and then use the Pythagorean theorem to find the resultant displacement. Let's break it down step-by-step:
South-West Movement : The particle moves 4 2 meters in the South-West direction. This can be split into components:
South component: 4 meters (since sin ( 4 5 ∘ ) = cos ( 4 5 ∘ ) = 2 1
West component: 4 meters
Upward Movement : The particle moves 12 meters upward. This affects only the vertical component.
East Movement : The particle then moves 1 meter East.
Next, we calculate the net displacement:
The net East-West move becomes ( 1 − 4 ) meters = − 3 meters (net 3 meters to the West).
The net North-South move is − 4 meters (since it's only Southward).
The net vertical move is 12 meters upward.
Using these net components, we can now find the net displacement using the 3D version of the Pythagorean theorem:
Net Displacement = ( − 3 ) 2 + ( − 4 ) 2 + ( 12 ) 2
= 9 + 16 + 144
= 169 = 13 meters
Therefore, the net displacement of the particle is 13 meters. The correct multiple-choice option is (A) 13 m .
