Question

What is your angular position 75 seconds after the wheel starts turning, measured counterclockwise from the top? Express your answer as an angle between 0∘ and 360∘. Express your answer in degrees.

Answer 1

Complete Question

A Ferris wheel on a California pier is 27 m high and rotates once every 32 seconds in the counterclockwise direction. When the wheel starts turning, you are at the very top.

What is your angular position 75 seconds after the wheel starts turning, measured counterclockwise from the top? Express your answer as an angle between 0∘ and 360∘. Express your answer in degrees.

Answer:

$\phi=123.75$

Explanation:

From the question we are told that:

Height $h=27m$

Period $T=32sec$

Time $t=75sec$

Generally the equation for angular velocity is mathematically given by

$\omega=\frac{2 \pi}{T}$

$\omega=\frac{2 \pi}{32}$

$\omega=0.196rad/s$

Therefore

$\theta=\omega t$

$\theta=0.196rad/s*75sec$

$\theta=843.75 \textdegree$

Therefore

$\phi=\theta-2(360)$

$\phi=123.75$