Final answer:
To find the resultant vector from Fx = 50 N and Fy = 15 N, calculate the magnitude using the Pythagorean theorem (approximately 52.2 N), and find the direction using the arctangent function (about 16.7 degrees to the horizontal).
Step-by-step explanation:
To find the magnitude and direction of the resultant vector when the components are Fx = 50 N and Fy = 15 N, we first apply the Pythagorean theorem. The magnitude (Fnet) is calculated by the square root of the sum of the squares of the components:
Fnet = √(Fx² + Fy²)
Fnet = √(50 N² + 15 N²) = √(2500 N² + 225 N²) = √(2725 N²) = 52.2 N (approx).
To determine the direction (θ), we use the arctangent function (tan⁻¹ or atan), which gives the angle in radians or degrees:
θ = tan⁻¹(Fy / Fx) = tan⁻¹(15 N / 50 N)
θ = tan⁻¹(0.3) ≈ 16.7° (to the horizontal axis).
Thus, the resultant vector has a magnitude of approximately 52.2 N and makes an angle of about 16.7° with the horizontal axis.