1. Consider a boat in the ocean, which is carrying contraband. Near to this boat is a lighthouse on a small island, which is attempting to track this boat with its searchlight. This ray of light originates at the lighthouse, and passes through the boat's position precisely at all times. The boat tries to escape the lighthouses' tracking by moving at a constant angle relative to the ray of light. (a) Write a differential equation which ocean. You may assume that 0 = or models the boat's path through the ㅠ 3π 2' 2 Hint: It may be helpful to consider the angle a(t) between the lighthouse and the boat at time t. π (b) Suppose and is first discovered at the position 3 kilometres east, and 4 kilometres to the north of the lighthouse. Solve for the curve that the boat travels along. Write your answer in polar coordinates. ㅠ 2 - (c) Sketch the direction field of the ODE if curves, i.e solution curves, in this case? = What are the integral (d) With with arbitrary consider the direction field, and a circle of arbitrary radius within the direction field. Conclude for which values of 0 will the boat's distance from the lighthouse increase over time.
1. Consider a boat in the ocean, which is carrying contraband. Near to this boat is a lighthouse on a small island, which is attempting to track this boat with its searchlight. This ray of light originates at the lighthouse, and passes through the boat's position precisely at all times. The boat tries to escape the lighthouses' tracking by moving at a constant angle relative to the ray of light. (a) Write a differential equation which ocean. You may assume that 0 = or models the boat's path through the ㅠ 3π 2' 2 Hint: It may be helpful to consider the angle a(t) between the lighthouse and the boat at time t. π (b) Suppose and is first discovered at the position 3 kilometres east, and 4 kilometres to the north of the lighthouse. Solve for the curve that the boat travels along. Write your answer in polar coordinates. ㅠ 2 - (c) Sketch the direction field of the ODE if curves, i.e solution curves, in this case? = What are the integral (d) With with arbitrary consider the direction field, and a circle of arbitrary radius within the direction field. Conclude for which values of 0 will the boat's distance from the lighthouse increase over time.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
Transcribed Image Text:1. Consider a boat in the ocean, which is carrying contraband. Near to this boat
is a lighthouse on a small island, which is attempting to track this boat with its
searchlight. This ray of light originates at the lighthouse, and passes through the
boat's position precisely at all times. The boat tries to escape the lighthouses'
tracking by moving at a constant angle relative to the ray of light.
(a) Write a differential equation which
π
ocean. You may assume that 0 = or
2' 2
Hint: It may be helpful to consider the angle a(t) between the lighthouse
and the boat at time t.
models the boat's path through the
3π
ㅠ
4'
=
(b) Suppose
and is first discovered at the position 3 kilometres east,
and 4 kilometres to the north of the lighthouse. Solve for the curve that
the boat travels along. Write your answer in polar coordinates.
ㅠ
(c) Sketch the direction field of the ODE if
curves, i.e solution curves, in this case?
=
2
What are the integral
(d) With with arbitrary consider the direction field, and a circle of arbitrary
radius within the direction field. Conclude for which values of 0 will the
boat's distance from the lighthouse increase over time.
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