Thread: Need some help on this deviative word problem

1. Need some help on this deviative word problem

A highway patrol plane is flying 3 miles above a level, straight road at a steady ground speed of 120 mph. The pilot sees an oncoming car and determines with radar that the line-of-sight distance from the plane to the car is 5 miles and decreasing at the rate of 160 mph. If the posted highway speed limit is 55 mph, should the motorist be fined for speeding? Why?

thanks......

2. Can you express x as a function of z? Then focus on the chain rule...

Just in case a picture helps with the logic of this...

... where

... the chain rule. Straight continuous lines differentiate downwards (integrate up) with respect to x, and the straight dashed line similarly but with respect to the dashed balloon expression (the inner function of the composite which is subject to the chain rule).

Spoiler:

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Don't integrate - balloontegrate!

http://www.ballooncalculus.org/examples/reference.html

http://www.ballooncalculus.org/asy/doc.html