1. ## related rates!

A highway patrol plane flies 1 mile above a straight section of rural interstate highway at a steady ground speed of 120 miles per hour. The pilot sees an oncoming car and, with radar, determines that the line-of-sight distance from the plane to the car is 1.5 miles and that this distance is decreasing at a rate of 136 miles per hour. Should the driver of the car be given a ticket for speeding?

2. Originally Posted by cottekr
A highway patrol plane flies 1 mile above a straight section of rural interstate highway at a steady ground speed of 120 miles per hour. The pilot sees an oncoming car and, with radar, determines that the line-of-sight distance from the plane to the car is 1.5 miles and that this distance is decreasing at a rate of 136 miles per hour
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Use Pythagoras and your given info to set up the problem and find the rate

at which the driver is going.

The hypoteneuse of the triangle formed is length 3/2 and dD/dt=-136.

dy/dt=0 because the chopper is at a constant height of y=1.

Since y=1 and D=3/2, then use Pythagoras to find the horizontal distance

the car is from the chopper.

The chopper is flying at 120 if we label that side of the triangle x and let

dx/dt=120. The trick is noting that the chopper and the car are

approaching one another. The chopper at dx/dt=120 and the car at, say, dz/dt=?

That is what must be found.

Should the driver of the car be given a ticket for speeding?
That depends. What's the speed limit and how hard-nosed is the cop?.