Answer:
11.17 ft
Step-by-step explanation:
Since the swing hangs from a beam 10 feet high with the seat hanging 2 feet above the ground, the swing moves in an arc of radius r = 10 ft - 2 ft = 8 ft.
Now, since the swing moves back and forth from -130° to -50° to the horizontal, the length of arc L it moves in is given by
L = Δθ/360 × 2πr where Δθ = change in angle of the swing = θ₂ - θ₁ where θ₁ = -50° and θ₂ = -130°. So, Δθ = θ₂ - θ₁ = -130° -(-50°) = -130° + 50° = -80°.
Substituting r and Δθ into L, we have
L = -80°/360° × 2π(8 ft)
= -8/36 × 16π ft
= -32π/9 ft
= -100.53/9 ft
= -11.17 ft
Ignoring the negative sign, the length of arc L = 11.17 ft. So, the swing moves back and forth 11.17 ft
