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# Pursuit curves and arc length question - help! watch

1. I am studying pursuit curves where a fast pirate ship which pursues a heavily laden treasure ship which tracks along a straight line. The ratio of the speeds of the ships is r > 1 (which is fixed) and the pirate captain spies the treasure ship initially at a distance d km away.

There s a step within the calculations that I am failing to understand:

I do not understand why or how the speed is equal to r(dY/dt)

Any help is greatly appreciated! thank you
2. (Original post by Kaya_01)
I am studying pursuit curves where a fast pirate ship which pursues a heavily laden treasure ship which tracks along a straight line. The ratio of the speeds of the ships is r > 1 (which is fixed) and the pirate captain spies the treasure ship initially at a distance d km away.

There s a step within the calculations that I am failing to understand:

I do not understand why or how the speed is equal to r(dY/dt)

Any help is greatly appreciated! thank you
I'm not an expert on this, but aren't they just putting in symbols the statement that the pirate ship's speed is r times the speed of the treasure ship?

The treasure ship is given to be moving in a straight line, presumably in the y-direction, so its speed is dy/dt; the pirate ship moves along an arc and in time t it has travelled arc length s, so its rate of motion ("speed") is just ds/dt.

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Updated: April 12, 2013
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