A police helicopter is flying due north at 100 mi/h and at a constant altitude o

Question

A police helicopter is flying due north at 100 mi/h and at a constant altitude of 1/2 mi. Below, a car is traveling west on a highway at 75 mi/h. At the moment the helicopter crosses over the highway, the car is 4 mi east of the helicopter. How fast is the distance between the car and helicopter changing at the moment the helicopter crosses the highway? [Round your answer to 1 decimal place.] The distance between the car and the helicopter is changing at a rate of mi/h at the moment the helicopter crosses the highway. Is the distance between the car and helicopter increasing or decreasing at that moment?

Explanation / Answer

Origin= crossing

Coordinates of helicopter(along y-axis,North dirn) = (0,y,0.5)

Coordinates of car(along x-axis) = (x,0,0)

x2 + y2 +0.52=d2

d=distance b/w the two vehicles

differentiating,

x.x` + y.y` = d.d`

4*(-75) + 0 = 0.52+42 * d`

a) d` = -74.42 mil/h

b) Distance between them is DECREASING

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