Question

If the horizontal components of three vectors are given by 1, 2 and 3 N and vertical components are 1, 3 and 4 N respectively then the magnitude of the resultant force is​

Answer 1

Answer:

Assume that the chain is exerting a 60 N force upon Fido at an angle of 40 degrees above the horizontal. A quick sketch of the situation reveals that to determine the vertical component of force, the sine function can be used and to determine the horizontal component of force, the cosine function can be used.

Answer 2

Given: Horizontal component of force = 1, 2, and 3 N

           The vertical component of force = 1, 3, and 4 N

To find: Magnitude of the resultant force

Solution: Net force in horizontal = 1 + 2 + 3 = 6N

Net force in vertical direction = 1 + 3 + 4 = 8N

The angle between the horizontal and vertical component is 90°

The resultant vector is equal to the vector summation of all the forces acting at a point.

The magnitude of the resultant force will be equal to = $\sqrt{F1+F2 + 2F1F2Cos90}$   ( cos90° = 0)

where F₁ is the horizontal force which is equal to 6N

F₂ is the vertical force which is equal to 8N

Putting the value in the equation,

= $\sqrt{6^2 + 8^2 + 0}$

= $\sqrt{36 + 64}$

=$\sqrt{100}$

= 10N

Therefore, the magnitude of the resultant force is 10N