Answer:
The resultant displacement is 5.8 cm, 31° South of the West axis ⇒ 4th
answer
Explanation:
A resultant vector is the combination of two or more single vectors
If the two vectors are perpendicular, then
The magnitude of the resultant vector = [tex]\sqrt{x^{2}+y^{2}}[/tex],where
x represents the horizontal vector and y represents the vertical vector
The direction of the resultant vector is [tex]tan^{-1}\alpha[/tex], where α
is the angle between the horizontal vector and the resultant vector
Vector 1 is 5 cm due to West-axis
Vector 2 is 3 cm due to South-axis
We need to find the resultant displacement of them
The West and South are perpendicular
The West is the horizontal vector and South is the vertical vector
The magnitude of the resultant displacement s is:
[tex]s=\sqrt{(5)^{2}+(3)^{2}}[/tex]
[tex]s=\sqrt{25+9}[/tex]
[tex]s=\sqrt{34}=5.8[/tex]
The direction of the resultant displacement s is:
[tex]tan^{-1}\frac{3}{5}=31[/tex]° south of the west (between the west and
the resultant displacement)
The resultant displacement is 5.8 cm, 31° South of the West axis
