Question

Bethany, who weighs 420 N, lies in a hammock suspended by ropes tied to two trees. The left rope makes an angle of 45∘ with the ground; the right one makes an angle of 30∘.

Answer 1

Take T_L and T_R as the tensions in the left and right ropes. Equilibrium gives

- horizontal: T_L cos45° = T_R cos30°
- vertical: T_L sin45° + T_R sin30° = 420 N

From the first, T_L = (cos30°/cos45°) T_R. Substitute into the vertical equation:

T_R( cos30° + sin30° ) = 420 N

So
T_R = 420 / (cos30° + sin30°) = 840 / (√3 + 1) = 420(√3 − 1) ≈ 307 N.

Then
T_L = (cos30°/cos45°) T_R ≈ 1.2247449 × 307 N ≈ 377 N.

Answers: T_left ≈ 377 N, T_right ≈ 307 N.