A 82.0-kg person, hanging from a rope, is being pulled away from a burning build

Question

A 82.0-kg person, hanging from a rope, is being pulled away from a burning building by a firefighter, as shown in the figure below. (a) Calculate the tension in the section of the rope between the building and the person being rescued (T1), if the person is momentarily motionless. The rope is attached to the roof of the building and hangs at a 15° angle from the side of the building. (Enter the magnitude only.) N (b) Calculate the tension in the section of the rope between the person being rescued and the firefighter (T2), if the person is momentarily motionless. The rope rises 10° between the person being rescued and the firefighter. (Enter the magnitude only.)

Explanation / Answer

Horizontal analysis:
T1 sin 15 = T2 cos 10
0.2588 T1 = 0.9848 T2
T2 = 0.2628 T1

Vertical analysis:
T1 cos 15 + T2 sin 10 = m g
T1 cos 15 + T2 sin 10 = 82 x 9.8
0.9659 T1 + 0.1736 T2 = 803.6

Combine those 2 equation:
0.9659 T1 + 0.1736 (0.2628 T1) = 803.6
0.9659 T1 + 0.0456 T1 = 803.6
T1 = 794.5 N

T2 = 0.2628 T1 = 208.8 N

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