   Chapter 2.8, Problem 48E

Chapter
Section
Textbook Problem

# Two people start from the same point. One walks east at 3 mi/h and the other walks northeast at 2 mi/h. How fast is the distance between the people changing after 15 minutes?

To determine

To find:

How fast is the distance between people changing after 15 minutes?

Explanation

1. Given:Let c denote the distance of first person from starting point and b denote the distance of second person from the  starting point at a given time then,dcdt= 3mi/h,dbdt= 2 mi/h

2. Calculations:

The figure is as shown below.

At  t = 15 min = 0.25 hours, the distances from point A are

b = 2 mi/h * 0.25 h = 0.5 mi

c = 3 mi/h * 0.25 h = 0.75 mi

Using law of cosine

a2= b2+ c2-2bc cos(45)

a2= b2+ c2-2bc (2 /2)

a= (b2+ c2-

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