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Final

Engineering Science 1036A/B Study Guide - Final Guide: Sailing ShipExam


Department
Engineering Science
Course Code
ENGSCI 1036A/B
Professor
Quazi Rahman
Study Guide
Final

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5.5 Optimization Problems - Minimum Distance
1. A power line is to be constructed from the shore of a lake to an island that is 500m away. The closest
power line ends 4 km along the shore form the point on the shore closest to the island. If it costs 5 times
as much to lay the power line under water as along the shore, how should the line be installed to minimize
the cost?)
2. A man lives on an island 1 km from the mainland. His favourite pub is 3 km along the shore from the point
on the shore closest to the island. The man can paddle his canoe at 3 km/h and can jog at 5 km/h.
Determine where he should land so as to reach the pub in the shortest possible time.
3. A sailing ship is 25 km due north of a drifting derelict vessel. If the sailing ship sails south at 4 km/hs while
the derelict drifts east at 3 km/h, find the distance of closest approach of the two ships. (i.e. find the
distance between the two ships when that distance is a minimum)
Solutions
1.
64
1
km from point closest to island, or 0.1 km 0≤x4
2. 0.75 km, 0≤x3
3. 15 km 0<t<6.25
22.
2
7
,
2
43
,
2
7
,
2
43
23. Lay pipe 465.4m along the shore from A, then lay the pipe from this point to B underwater
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