Assignment #9

Due: 10 March, 1998

"My name is Blond, Thames Blond."

Thames Blond, playboy heir to the Pale River Ale fortune and not-so-secret agent of MI7, is cruising along one of Saskatchewan's famously straight roads in his BMW at its top speed of 200 km/h, approaching the point where one of Saskatchewan's famously straight railroads crosses the road at a right angle. The last car of a train is just passing the crossing at a speed of 100 km/h just as Blond is 1 km away. At this instant, Blond spots the infamous Dr. Yes looking out the back of that last train car. He immediately swerves to follow *, keeping his BMW headed towards the last car of the train until he catches up. (We leave the question of what happens after that to your imagination...)

1. If the train and Blond maintain their speeds of 100 km/h and 200 km/h, how far from the crossing does Blond catch up with the train? [10]

Hint: Supposing that the road lies along the x-axis and the railroad track along the y-axis, show that the BMW's path is the graph of a function satisfying the differential equation

2xy'' = square root (1 + [y']^2).

Solve this equation, assuming that y = 0 and y' = 0 when x = 1, and take it from there...

Bonus. The ends of a piece of string 10 units long are attached to the points (-4,0) and (4,0) in the plane. A pencil is used to stretch the string taught along the plane and then run all the way around the two points, keeping the string taught at all times. What curve does the pencil trace out? Explain, in detail, why! [1]

* Remember that Saskatchewan is famously flat...

Solution to Assignment #9
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Maintained by Stefan Bilaniuk. Last updated 1998.08.22.