Question

Your friend has slipped and fallen. To help her up, you pull with a force F, as the drawing shows. The vertical component of this force is 110 newtons (N), while the horizontal component is 122 N. Find (a) the magnitude of F and (b) the angle0.

Answer 1

This question can be solved using the concept of the composition of the vector.

(a) The magnitude of F is b "164.27 N".

(b) The angle of the vector from horizontal is " ".

(a)

From the composition of the rectangular components of a vector, we know that the magnitude of the resultant vector is given by the following formula:

$F = \sqrt{F_x^2+F_y^2}$

where,

$F_x$ = x-component of the force = 122 N

$F_y$ = y-component of the force = 110 N

Therefore,

$F = \sqrt{(122\ N)^2+(110\ N)^2}$

F = 164.27 N

(b)

The angle of the vector is given by the following formula:

$\theta = tan^{-1}(\frac{F_y}{F_x})\\\\\theta = tan^{-1}(\frac{110\ N}{122\ N})$

θ = 42.04°

Learn more about the composition of vector here:

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