Chapter 4, Problem 1PS

(a)

To determine

To find: the angle through which the dinner party rotated.

Answer to Problem 1PS

  $990°\text{rotation}$

Explanation of Solution

Given information:

The restaurant at the top of the space Needle in Seattle, Washington is circular and has a radius of 47.25 feet. The dining part of the restaurant revolves, making about one complete revolution every 48 minutes. A dinner party, seated at the edge of the revolving restaurant at 6.45 P.M, finishes at 8.57 P.M.

Calculation:

Number of revolutions made by the restaurant are

  $\begin{array}{l}=\frac{132}{48}\\ =\frac{11}{4}\end{array}$

As, 1 revolution means $360°$ rotation,

Therefore, $\frac{11}{4}$ revolutions means,

  $\begin{array}{c}\frac{11}{4}\left(360°\right)\\ =11\left(90°\right)\\ =990°\text{rotation}\end{array}$

(b)

To determine

To find: the distance the party traveled during dinner.

Answer to Problem 1PS

The distance travelled during the dinner is,

  $816.42$ feet

Explanation of Solution

Calculation:

Distance travelled in 1 revolution is,

  $\begin{array}{c}2\pi r=2\pi \left(47.25\right)\\ =296.88\text{feet}\end{array}$

Hence, the distance travelled during the dinner is,

  $\begin{array}{l}=\frac{11}{4}\left(296.88\right)\\ =816.42\end{array}$