Final answer:
The magnitude of the resultant force is 50.0 N, and its direction is approximately 53.13° above the horizontal to the left.
Step-by-step explanation:
To find the magnitude and direction of the resultant force produced by a vertically upward force of 40 N and a left horizontal force of 30 N, we can use the Pythagorean theorem and trigonometry. Since the two forces are perpendicular to each other, the magnitude of the resultant force (Fnet) is the hypotenuse of a right triangle with sides of 40 N and 30 N.
To calculate the magnitude:
- Fnet = √(40 N)² + (30 N)²
- Fnet = √1600 N² + 900 N²
- Fnet = √2500 N²
- Fnet = 50.0 N
To find the direction (angle θ) with respect to the horizontal:
- θ = tan-1(Opposite/Adjacent)
- θ = tan-1(40 N / 30 N)
- θ ≈ 53.13° above the horizontal to the left.