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A box with a mass of [tex]$m = 89$[/tex] kilograms is being pulled by a constant force of [tex]$f = 190$[/tex] newtons at an angle [tex]$\theta = 33^\circ$[/tex]. The initial speed of the box is zero m/s.

What is the horizontal component of the force?

A. [tex]190 \sin(33^\circ)[/tex]

B. [tex]33 \sin(190^\circ)[/tex]

C. [tex]33 \cos(190^\circ)[/tex]

D. [tex]190 \cos(33^\circ)[/tex]

Answer :

Final answer:

The horizontal component of a force applied at an angle is calculated by multiplying the force by the cosine of the angle. Thus, for a force of 190 newtons applied at 33 degrees, the horizontal component is 190 cos(33°).

Explanation:

In the given problem, a force is applied at an angle, and we are asked to find the horizontal component of this force. The horizontal component of any force F applied at an angle θ is calculated using the formula F cos(θ). Therefore, for a force of 190 newtons being applied at an angle of 33 degrees, the horizontal component is 190 cos(33°).

This is because the cos(θ) function gives the adjacent side in a right-angled triangle, which in this case is the horizontal component of the force. A force applied at an angle can always be broken down into its vertical (F sin θ) and horizontal (F cos θ) components, which simplifies calculations. So, the correct choice is d) 190 cos(33°).

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