A port and a radar station are 5 mi apart on a straight shore running east and west. A ship leaves the port at noon traveling at a rate of 25 mi/hr. If the ship maintains its speed and course, what is the rate of change of the tracking angle 0 between the shore and the line between the radar station and the ship at 12:30 PM? (Hint: Use the law of sines.) Northeast course 45° Port Radar station + S mi Use the Law of Sines to find an equation relating the angle, 0, the angle that the ship left the port at, the distance between the radar system and the ship, a, and the distance between the port and the ship, s. Evaluate any known trigonometric functions of 45° as needed. Use radians to express any other angles. - 1 0=x- sin (Type an exact answer, using x as needed.) Differentiate both sides of the equation with respect to t, evaluating any trigonometric functions of (45°) as needed. d0 ds da av2a? -2 dt dt dt The rate of change of the tracking angle between the shore and the line between the radar station and the ship at 12:30 PM is (Round to four decimal places as needed.)
A port and a radar station are 5 mi apart on a straight shore running east and west. A ship leaves the port at noon traveling at a rate of 25 mi/hr. If the ship maintains its speed and course, what is the rate of change of the tracking angle 0 between the shore and the line between the radar station and the ship at 12:30 PM? (Hint: Use the law of sines.) Northeast course 45° Port Radar station + S mi Use the Law of Sines to find an equation relating the angle, 0, the angle that the ship left the port at, the distance between the radar system and the ship, a, and the distance between the port and the ship, s. Evaluate any known trigonometric functions of 45° as needed. Use radians to express any other angles. - 1 0=x- sin (Type an exact answer, using x as needed.) Differentiate both sides of the equation with respect to t, evaluating any trigonometric functions of (45°) as needed. d0 ds da av2a? -2 dt dt dt The rate of change of the tracking angle between the shore and the line between the radar station and the ship at 12:30 PM is (Round to four decimal places as needed.)
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section6.2: Trigonometric Functions Of Angles
Problem 81E
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Question
A port and a radar station are 5 mi apart on a straight shore running east and west. A ship leaves the port at noon traveling at a rate of 25 mi/hr. If the ship maintains its speed and course, what is the rate of change of the tracking angle θ between the shore and the line between the radar station and the ship at 12:30 PM?
Please help me with the last question. I figured out the first two questions but I do not know the answer for the last question as you can see in the image.
Transcribed Image Text:A port and a radar station are 5 mi apart on a straight shore running east and west. A ship leaves the port at noon traveling at a rate of 25 mi/hr. If the ship maintains its speed and course,
what is the rate of change of the tracking angle 0 between the shore and the line between the radar station and the ship at 12:30 PM? (Hint: Use the law of sines.)
Northeast
course
45°
IB
Port
Radar station
e 5 mi
Use the Law of Sines to find an equation relating the angle, 0, the angle that the ship left the port at, the distance between the radar system and the ship, a, and the distance between the port and the ship, s. Evaluate any known trigonometric
functions of 45° as needed. Use radians to express any other angles.
0 = T - sin
(Type an exact answer, using n as needed.)
Differentiate both sides of the equation with respect to t, evaluating any trigonometric functions of (45°) as needed.
de
1
ds
da
%3D
a
S
dt
dt
dt
2
av 2a
- S
The rate of change of the tracking angle 0 between the shore and the line between the radar station and the ship at 12:30 PM is
(Round to four decimal places as needed.)
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