Resolving forces into vertical and horizontal components

Steps:

• Resolve the 10 N force as 10 N vertical and 0 N horizontal.
• Resolve the 8 N force at 40° to vertical: vertical component = 8 cos 40°, horizontal component = 8 sin 40°.
• Net vertical component = 10 N - 8 cos 40° (components oppose based on diagram).
• Resultant magnitude = √[(net vertical)² + (horizontal)²]; angle to vertical = tan⁻¹(horizontal / net vertical).

Why D is correct:

• D matches the vector addition formula for opposing vertical components, yielding magnitude ≈6.8 N and direction ≈36° to vertical via Pythagorean theorem and arctangent.

Why the others are wrong:

• A: Magnitude too large; assumes adding vertical components instead of opposing.
• B: Angle close but magnitude too large; ignores opposition of vertical components.
• C: Angle reasonable but magnitude incorrect; misapplies component resolution values.

Final answer: D