Taxi Cab Vectors

356 MHR • Calculus and Vectors • Chapter 6

Eighth pages

356 MHR • Calculus and Vectors • Chapter 6

TA S K Taxi Cab Vectors

A taxi has three passengers when it starts at A. It must drop off two people at B and the third at C. The arrows represent one-way streets.

a) Using vectors, find two different routes that go from A to C via B.

b) Show that the total displacement is equal in each case.

In the taxi, travelling northbound takes 12 min per block, travelling southbound takes 5 min per block, travelling westbound takes 6 min per block, travelling eastbound takes 8 min per block, and travelling northeast or southwest takes 10 min per block.

c) Which of your routes takes less time?

d) Is there a best route? Is it unique?

e) Identify which vector properties are used in your solution.

f) If the taxi charges for mileage are $0.50/rectangular block and the time charges are $0.10/minute, what is the cheapest route from A to C? How much should each passenger pay?