1. A straight river flows east at a speed of 20mi/h. A boater starts at the south shore of the river and heads in the direction which is 60° to the south shore. The motorboat has a speed 20 mi/h relative to the water. (a) Express the velocity of the river as a vector in component form; (b) Express the velocity of the motorboat relative to the water as a vector in component form; (c) Find the true velocity of the motorboat;
1. A straight river flows east at a speed of 20mi/h. A boater starts at the south shore of the river and heads in the direction which is 60° to the south shore. The motorboat has a speed 20 mi/h relative to the water. (a) Express the velocity of the river as a vector in component form; (b) Express the velocity of the motorboat relative to the water as a vector in component form; (c) Find the true velocity of the motorboat;
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter8: Applications Of Trigonometry
Section8.3: Vectors
Problem 45E
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![1. A straight river flows east at a speed of 20mi/h. A boater starts at the south shore of the
river and heads in the direction which is 60° to the south shore. The motorboat has a
speed 20 mi/h relative to the water.
(a) Express the velocity of the river as a vector in component form;
(b) Express the velocity of the motorboat relative to the water as a vector in component form;
(c) Find the true velocity of the motorboat;
(d) Find the true speed of the motorboat;
(e) Find the true direction of the motorboat (the bearing).
Answer: (a) w = (20,0) = 207 + 0j ; (b) ở = (10,10/3) = 107 + 10v3j; (c) ủ = (30,10V3) = 307 + 10/3j
(d) [ū] = 20V3 mi/h , (e) let the angle between the true velocity and the horizontal axis is 0;
b
then tan 0 =
V3
,0 = 30° ; a = 90° – 0 = 60°; So, N 60° E.
a
60°](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F185bed84-dcb2-447b-b8ea-e98e060347ec%2Fc84a5e35-5a55-4305-8ac5-55f7e93e3099%2Fxi7y61l_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1. A straight river flows east at a speed of 20mi/h. A boater starts at the south shore of the
river and heads in the direction which is 60° to the south shore. The motorboat has a
speed 20 mi/h relative to the water.
(a) Express the velocity of the river as a vector in component form;
(b) Express the velocity of the motorboat relative to the water as a vector in component form;
(c) Find the true velocity of the motorboat;
(d) Find the true speed of the motorboat;
(e) Find the true direction of the motorboat (the bearing).
Answer: (a) w = (20,0) = 207 + 0j ; (b) ở = (10,10/3) = 107 + 10v3j; (c) ủ = (30,10V3) = 307 + 10/3j
(d) [ū] = 20V3 mi/h , (e) let the angle between the true velocity and the horizontal axis is 0;
b
then tan 0 =
V3
,0 = 30° ; a = 90° – 0 = 60°; So, N 60° E.
a
60°
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