Mathematics

Mathematics

Problem

A force has components Fx=−6 NF_x=-6\,\text{N} and Fy=−8 NF_y=-8\,\text{N}. Determine the magnitude of the force and the angle it makes with the +x+x-axis (measured anticlockwise, 0∘≤θ<360∘0^{\circ}\leq\theta<360^{\circ}). a) 10 N,  053∘10\,\text{N},\;053^{\circ} b) 10 N,  127∘10\,\text{N},\;127^{\circ} c) 10 N,  233∘10\,\text{N},\;233^{\circ} d) 14 N,  233∘14\,\text{N},\;233^{\circ}
Intuitive explanation

This problem is about reconstructing a vector's size and direction from its components. The magnitude comes straight from the Pythagorean theorem applied to the two perpendicular components, while the angle requires you to use inverse tangent and pay careful attention to which quadrant the force vector actually lives in—both components are negative, so you're in the third quadrant, not the first.

Intuitive explanation

This problem is about reconstructing a vector's size and direction from its components. The magnitude comes straight from the Pythagorean theorem applied to the two perpendicular components, while the angle requires you to use inverse tangent and pay careful attention to which quadrant the force vector actually lives in—both components are negative, so you're in the third quadrant, not the first.

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