Work by angled force on horizontal displacement

Steps:

• Identify work as the horizontal component of tension times horizontal distance: W = T × d × cosθ.
• Tension T = 100 N, distance d = 5 m, angle θ = 30° with horizontal.
• Calculate cos30° = √3/2 ≈ 0.866.
• W = 100 × 5 × 0.866 = 433 J, rounds to 430 J.

Why C is correct:

• Work is force parallel to displacement times distance; cos30° isolates the horizontal component of tension per the dot product definition.

Why the others are wrong:

• A: 250 J uses cos60° (wrong angle) or halves the force incorrectly.
• B: 290 J from erroneous cos30° approximation (e.g., 0.58 instead of 0.866).
• D: 500 J is T × d without cosθ, treating force as fully horizontal.

Final answer: C