   Chapter 1.3, Problem 57E ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

#### Solutions

Chapter
Section ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

# A ship is at a speed of 30km/h parallel to a straight shoreline. The ship is 6 km from shore and it passes a lighthouse at noon(a) Express the distance s between the lighthouse and the ship as a function of d, the distance the ship has traveled since noon; that is, find f so that s =f(d).(b) Express d as a function of t, the time elapsed since noon; that is, find g so that d = q(t).(c) Find f ◦ g. What does this function represent?

(a)

To determine

To express: The distance between the lighthouse and the ship as a function of d.

Explanation

Given:

The speed of the ship is 30 km/h.

The distance between the ship and shore is 6 km.

Diagram:

Draw a rough diagram to indicate the positions of the ship, lighthouse and shore as shown below in Figure 1.

Consider the right triangle from Figure 1.

In order to find the distance s, use Pythogorean theorem.

s2=d2+62

(b)

To determine

To express: The function d as a function of t where t is the time elapsed since noon.

(c)

To determine

To find: The composition function fg and explain.

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