Question

Two gates are fitted at the entrance of a library. To open the gates easily, a wheel is fixed at 6 feet distance from the wall to which the gate is fixed. If one of the gates is opened to 90°, find the distance moved by the wheel (π = 3.14)

Answer 1

Let A be the position of the wall AC be the gate in initial position and AB be position when it is moved 90°.

Now the arc length BC gives the distance moved by the wheel.

Length of the arc = `theta^circ/(360^circ) xx 2pi"r units"`

= `(90^circ)/(360^circ) xx 2 xx 3.14 xx 6  "feet"`

= 3.14 × 3 feet

= 9.42 feet

∴ Distance moved by the wheel = 9.42 feet.