Chapter 8.1, Problem 57PS

Solution

To calculate : The times during which the car is in range of the tower.

The car is in range of the tower for $1.17\text{ hour}$ .

Given information :

At the time $t=0$ , a car begins travelling east at $60$ miles per hour from a point $100$ miles west and $40$ miles north of a radio tower. The tower has a transmission range of $50$ miles.

Formula used:

  $t=\frac{d}{s}$ , where $t=$ time, $d=$ distance, and $s=$ speed.

Calculation :

The graph given below describes the region covered by the tower.

  

So, the time during which the car is in range of the tower will be

  $\begin{array}{c}t=\frac{70}{60}\\ \approx 1.17\text{ hour}\end{array}$

Therefore, the car is in range of the tower for $1.17\text{ hour}$ .