Chapter 1.3, Problem 57E

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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.

(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

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