PRECALCULUS:GRAPHICAL,...-NASTA ED.
PRECALCULUS:GRAPHICAL,...-NASTA ED.
10th Edition
ISBN: 9780134672090
Author: Demana
Publisher: PEARSON
Expert Solution & Answer
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Chapter 5.6, Problem 53E
Solution

a.

The speed of each ship and express the answer in knots.

Speed of ship A is 15.1 knots and speed of ship B is 12.4 knots.

Given information:

Two ships leave the common port at 8:00 a.m. and travel at a constant rate of speed. The portions of the log for the both ships are shown in the table below.

   Time  Naut mi from Port  Naut mi from Ship B  Time  Naut mi from Port  Naut mi from Ship A 9:0015.18.79:0012.48.710:0030.217.311:0037.226.0

Calculation:

The distance of the ship from the port at 9:00 a.m. was 15.1 Naut mi. That means, the ship A travelled a distance of 15.1 Naut mi in one hour. So, the speed of the ship A is 15.1 knots.

Similarly, ship B traveled a distance of 12.4 Naut mi in one hour. So, its speed is 12.4 knots.

b.

The angle of the intersection of course of the two ships.

The angle of the intersection of course of the two ships is 35.18 .

Given information:

Two ships leave the common port at 8:00 a.m. and travel at a constant rate of speed. The portions of the log for the both ships are shown in the table below.

   Time  Naut mi from Port  Naut mi from Ship B  Time  Naut mi from Port  Naut mi from Ship A 9:0015.18.79:0012.48.710:0030.217.311:0037.226.0

Calculation:

The distance of the ship from the port at 9:00 a.m. was 15.1 Naut mi. That means, the ship A travelled a distance of 15.1 Naut mi in one hour

Similarly, ship B traveled a distance of 12.4 Naut mi in one hour.

Now, let θ be the angle of intersection of the course of the two ships. So, the triangle representing the distance of each ship from the port and the distance between them can be shown as shown below.

  PRECALCULUS:GRAPHICAL,...-NASTA ED., Chapter 5.6, Problem 53E , additional homework tip  1

Now, use the cosine formula to find the angle θ as shown below.

  AB2=AP2+BP22APBPcosθ8.72=15.12+12.42215.112.4cosθ75.69=228.01+153.76374.48cosθ37448cosθ=30608cosθ=38264681θ=cos138264681=35.179935.18

Therefore, the angle of the intersection of course of the two ships is 35.18 .

c.

The distance between the ships at 12:00 noon.

The ships are 34.8 Naut mi apart at 12:00 noon.

Given information:

Two ships leave the common port at 8:00 a.m. and travel at a constant rate of speed. The portions of the log for the both ships are shown in the table below.

   Time  Naut mi from Port  Naut mi from Ship B  Time  Naut mi from Port  Naut mi from Ship A 9:0015.18.79:0012.48.710:0030.217.311:0037.226.0

Calculation:

The distance traveled by ship A by 12:00 noon is 4×15.1=60.4 Naut mi, and by ship B is 4×12.4=49.2 Naut mi.

From part (b), the angle of intersection of the courses of the two ships is θ=35.18 .

So, the triangle representing the distance of each ship from the port and the distance between them can be shown as shown below.

  PRECALCULUS:GRAPHICAL,...-NASTA ED., Chapter 5.6, Problem 53E , additional homework tip  2

Now, use the cosine formula to find the distance AB between the ships.

  AB2=AP2+BP22APBPcosθAB2=60.42+49.22260.449.2cos35.18AB2=3648.16+2420.645943.36×0.8173AB2=3648.16+2420.64-4857.508128AB2=1211.291872AB=1211.291872AB=34.80361AB34.8

Therefore, the ships are 34.8 Naut mi apart at 12:00 noon.

Chapter 5 Solutions

PRECALCULUS:GRAPHICAL,...-NASTA ED.

Ch. 5.1 - Prob. 11QRCh. 5.1 - Prob. 12QRCh. 5.1 - Prob. 1ECh. 5.1 - Prob. 2ECh. 5.1 - Prob. 3ECh. 5.1 - Prob. 4ECh. 5.1 - Prob. 5ECh. 5.1 - Prob. 6ECh. 5.1 - Prob. 7ECh. 5.1 - Prob. 8ECh. 5.1 - Prob. 9ECh. 5.1 - Prob. 10ECh. 5.1 - Prob. 11ECh. 5.1 - Prob. 12ECh. 5.1 - Prob. 13ECh. 5.1 - Prob. 14ECh. 5.1 - Prob. 15ECh. 5.1 - Prob. 16ECh. 5.1 - Prob. 17ECh. 5.1 - Prob. 18ECh. 5.1 - Prob. 19ECh. 5.1 - Prob. 20ECh. 5.1 - Prob. 21ECh. 5.1 - Prob. 22ECh. 5.1 - Prob. 23ECh. 5.1 - Prob. 24ECh. 5.1 - Prob. 25ECh. 5.1 - Prob. 26ECh. 5.1 - Prob. 27ECh. 5.1 - Prob. 28ECh. 5.1 - Prob. 29ECh. 5.1 - Prob. 30ECh. 5.1 - Prob. 31ECh. 5.1 - Prob. 32ECh. 5.1 - Prob. 33ECh. 5.1 - Prob. 34ECh. 5.1 - Prob. 35ECh. 5.1 - Prob. 36ECh. 5.1 - Prob. 37ECh. 5.1 - Prob. 38ECh. 5.1 - Prob. 39ECh. 5.1 - Prob. 40ECh. 5.1 - Prob. 41ECh. 5.1 - Prob. 42ECh. 5.1 - Prob. 43ECh. 5.1 - Prob. 44ECh. 5.1 - Prob. 45ECh. 5.1 - Prob. 46ECh. 5.1 - Prob. 47ECh. 5.1 - Prob. 48ECh. 5.1 - Prob. 49ECh. 5.1 - Prob. 50ECh. 5.1 - Prob. 51ECh. 5.1 - 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