A vector has an x-component of - 3.09m and a y-component of 187. Find the magnitude and direction of the vector.

187 meters, 90.9 degrees

Explanation:

vx = - 3.09 m

vy = 187 m

Use Pythagorean theorem to find the magnitude:

v² = vx² + vy²

v² = (-3.09) ² + 187²

v² = 9.55 + 34969

v² = 34978.55

v = 187 meters

Use trigonometry to find the angle:

θ = atan (vy / vx)

θ = atan (187 / - 3.09)

θ = - 89.1°, 90.9°

Since θ is in the second quadrant, θ = 90.9°.

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