Will the beam clear the wires on its way to standing up straight? Explain.

Question

A construction crew wants to hoist a heavy beam so that it is standing up straight. They tie a rope to the beam, secure the base, and pull the rope through a pulley to raise one end of the beam from the ground. When the beam makes an angle of 408 with the ground, the top of the beam is 8 ft above the ground.

The construction site has some telephone wires crossing it. The workers are concerned that the beam may hit the wires. When the beam makes an angle of 608 with the ground, the wires are 2 ft above the top of the beam. Will the beam clear the wires on its way to standing up straight? Explain.

Answer 1

Let x = length of the beam

sin40° = 8/x

x = 12.446 ft

Let y = height of the end of the beam when the angle formed by the other end of the beam and the ground is 60°.

sin60° = y/12.446

y = 10.779 ft

Height of wires above ground = y + 2 = 12.779 ft

The vertical beam will clear the wires by about 12.779 ft - 12.446 ft ≈ 1/3 ft = 4" clearance