Question

An airplane is flying 600 mph on a horizontal path that will take it directly over an observer. The airplane remains a constant altitude of 7 miles. What is the rate of change of the distance between the observer and the airplane when X = 5 miles?

Answer 1

Change of the distance between the observer and the airplane when X = 5 miles is 348.84 mph

Explanation:

We have by Pythagoras theorem

Distance between the observer and the airplane² = Horizontal distance² + Altitude²

d² = h² + a²

Here we have

h = X = 5 miles

a = 7 miles

d² = 5² + 7² = 74

d =8.60 miles

`(dh)/(dt)=600mph\\\\(da)/(dt)=0`

Differentiating d² = h² + a² with respect to time

`2d(dd)/(dt)=2h(dh)/(dt)+2a(da)/(dt)\\\\8.60(dd)/(dt)=5* 600+7* 0\\\\(dd)/(dt)=348.84mph`

Change of the distance between the observer and the airplane when X = 5 miles is 348.84 mph