Answer:
[tex]a_{x} = 0.342 \frac{m}{ {s}^{2} } \: "x \: component \: of \: acceleration"
\: \\ a_{y} = 1.02 \: \frac{m}{ {s}^{2} } \: "y \: component \: of \: acceleration" [/tex]
Explanation:
Given a mass of 63.9kg with a total applied force of 125 N at a 31.5° inclination relative to the horizontal and vertical, and a horizontal resistance force of 84.8 N. The components of acceleration can be calculated as follows:
Force = mass × acceleration
Vertical component of a vector = vector × Sin(angle)
Horizontal component of a vector = vector × Cos(angle)
extra:
V = √x^2+y^2
θ (angle, "theta") = arctan or inverse tan(y/x) (For this instance. Theta is usually an angle measure though)
x = V cos θ
y = V sin θ
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To find the vertical component of acceleration we must first take the vector quantity of our force which is 125 N (Newtons) and it's angle of 31.5°.
Vertical force = 125 × sin(31.5 degrees) = 125 × 0.5225 = 65.312 N [aka the normal force]
This works because force is a vector, it has both direction(by the angle of force), and magnitude(it's quantity).
Then take the force equation, and rearrange it to solve for the upward acceleration: F = m × a → a = F/m.
a = 65.312/63.9 ≈ 1.02 m/s^2.
Then for the horizontal acceleration, take the cosine for the horizontal part
