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A boat leaves a port traveling due east at 12 mi/hr. At the same time, another boat leaves the same port traveling northeast at 15 mi/hr. The angle 8 of the line between the boats is measured relative to due north (see the figure to the right). What is the rate of change of this angle 30 min after the boats leave the port? 3 hr after the boats leave the port?

A boat leaves a port traveling due east at 12 mi/hr. At the same time, another boat leaves the same port traveling northeast at 15 mi/hr. The angle 8 of the line between the boats is measured relative to due north (see the figure to the right). What is the rate of change of this angle 30 min after the boats leave the port? 3 hr after the boats leave the port?

Advanced Engineering Mathematics
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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A boat leaves a port traveling due east at 12 mi/hr. At the same time, another boat leaves the same port traveling northeast at 15 mi/hr. The angle 8 of the line between the boats is measured relative to due north (see the figure to the right). What is the rate of change of this angle 30 min after the boats leave the port? 3 hr after the boats leave the port? X= Let x be the distance from the port to the eastbound boat and let z be the distance from the port to the northeast bound boat. Write an equation relating x, z, and 0. √√2 √2 2 (Type an exact answer. Type any angle measures in radians.) Z+ -z tan 0 2 C The rate of change of this angle 30 min after the boats leave the port is (Round to the nearest thousandth as needed.) Port 15 mi/h 12 mi/h ----191
Transcribed Image Text:A boat leaves a port traveling due east at 12 mi/hr. At the same time, another boat leaves the same port traveling northeast at 15 mi/hr. The angle 8 of the line between the boats is measured relative to due north (see the figure to the right). What is the rate of change of this angle 30 min after the boats leave the port? 3 hr after the boats leave the port? X= Let x be the distance from the port to the eastbound boat and let z be the distance from the port to the northeast bound boat. Write an equation relating x, z, and 0. √√2 √2 2 (Type an exact answer. Type any angle measures in radians.) Z+ -z tan 0 2 C The rate of change of this angle 30 min after the boats leave the port is (Round to the nearest thousandth as needed.) Port 15 mi/h 12 mi/h ----191
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