Final answer:
The resultant vector R is found by summing the horizontal and vertical components of the original vectors, then using the Pythagorean theorem and trigonometry to find the magnitude and direction. In this case, R has a magnitude of 10.7 m and a direction of 69.44° relative to the x-axis.
Step-by-step explanation:
To find the resultant of two vectors, we can break each vector into its horizontal (x) and vertical (y) components, sum those components, and then use the Pythagorean theorem and trigonometry to determine the magnitude and direction of the resultant vector R.
A. To draw the resultant from the start of the first vector to the end of the second, label it "R".
B. Xtotal = X₁ + X₂ = 9.2 m + (-5.2 m) = 4.0 m.
C. Ytotal = Y₁ + Y₂ = 7.7 m + 3 m = 10.7 m.
D. Calculate the magnitude (length) of R using the Pythagorean theorem:
R = √(Xtotal² + Ytotal²) = √(4.0 m² + 10.7 m²) = √(114.49 m²) = 10.7 m.
E. Calculate the direction of R relative to the x-axis:
θ = tan⁻¹ (Ytotal/Xtotal) = tan⁻¹ (10.7 m / 4.0 m) = tan⁻¹ (2.675) = 69.44°.