Chapter 9.3, Problem 31PPS

To determine

To find: The position of Jane after $31$ seconds.

Answer to Problem 31PPS

The position of Jane after $31$ seconds is $\left(2,-4\right)$ .

Explanation of Solution

The ride rotates at the rate of $0.25\text{rev}/\sec$ .

The can rotates at $0.5\text{rev}/\sec$ .

After $31\sec$ , the ride will have rotated,

  $31\times 0.75=7.75\text{times}$

So, Jane will in the bottom position of the ride with the car having center at $\left(0,-4\right)$ .

Also after $31\sec$ the car will have rotated,

  $31\times 0.5=15.5\text{times}$ .

So, Jane will be in the position direction across from her staring position.

Therefore, the position of Jane after

  $31$ seconds is $\left(2,-4\right)$ .