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Answer :
Final answer:
The vector components of the force exerted at 37 degrees below the horizontal are approximately 40 N in the x-direction and -30 N in the y-direction, corresponding to answer choice (c) 40 N, -30 N. Therefore, the correct answer is (c) 40 N, -30 N.
Explanation:
The vector components of the force exerted by a girl pushing a box with a force of 50 N at an angle of 37 degrees below the horizontal are determined by breaking the force into its horizontal (x-direction) and vertical (y-direction) components. The horizontal component (Fx) is found using the cosine of the angle:
Fx = F * cos(θ) = 50 N * cos(37°) = 50 N * 0.7986 ≈ 40 N
The vertical component (Fy) is found using the sine of the angle and will be negative since the force is below the horizontal:
Fy = -F * sin(θ) = -50 N * sin(37°) = -50 N * 0.6018 ≈ -30 N
Therefore, the correct answer is (c) 40 N, -30 N.
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