Chapter 9.3, Problem 32PPS

(a)

To determine

To find: The coordinates of Brandon and Nestor after $5$ seconds.

Answer to Problem 32PPS

The coordinates of Brandon and Nestor after $5$ seconds is $\left(100,100\sqrt{3}\right)$ .

Explanation of Solution

The rotation angle after $5\sec$ is,

  $\begin{array}{c}\theta =\frac{360°}{30}\times 5\\ =60°\end{array}$

The coordinates after $5$ seconds are,

  $\left(200\cos 60°,200\sin 60°\right)=\left(100,100\sqrt{3}\right)$

Therefore, the coordinates of Brandon and Nestor after $5$ seconds is $\left(100,100\sqrt{3}\right)$ .

(b)

To determine

To find: The winner of the race.

Answer to Problem 32PPS

The winner of the race is Brandon.

Explanation of Solution

Suppose tha t the length of the lap is $50$ laps and Brandon continues the race at the same rate.

Since, Brandon completes one lap in thirty seconds.

Fifty laps is completed in,

  $\begin{array}{c}Time=30\times 50\\ =1500\text{sec}\times \frac{1\text{min}}{60\text{sec}}\\ =25\text{minutes}\end{array}$

Therefore, the winner of the race is Brandon.