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2 years ago

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Your friend has slipped and fallen. To help her up, you pull with a force F, as the drawing shows. The vertical component of thi

s force is 110 newtons (N), while the horizontal component is 122 N. Find (a) the magnitude of F and (b) the angle0.

1 answer:

sineoko [7]2 years ago

3 0

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,

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

<u>F = 164.27 N</u>

(b)

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

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

<u>θ = 42.04°</u>

Learn more about the composition of vector here:

brainly.com/question/24313520?referrer=searchResults

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Answer with Explanation:

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Complete Question

A football coach walks 18 meters westward, then 12 meters eastward, then 28 meters westward, and finally 14 meters eastward.

a

From this motion what is the distance covered

b

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Answer:

a

$D = 72 \ m$

b

Magnitude

$d = - 20 \ m$

Direction

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Explanation:

From the question we are told that

The first distance covered westward is $d_w_1 = 18 \ m /tex] The first distance covered eastward is [tex]d_e1 = 12 \ m /tex] The second distance covered westward is [tex]d_w_2 = 28 \ m /tex] The second distance covered eastward is [tex]d_e2 = 14 \ m /tex] Generally the distance covered is mathematically represented as [tex]D = d_w1 + d_w2 + d_e1 + d_e2$

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=> $D = 72 \ m$

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The magnitude of the displacement is

$d = -d_w1 -d_w2 + d_e1 + d_e2$

=> $d = -18-28 + 12 + 14$

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