SOLUTION: 5. An airplane flies over an observer with a velocity of 400 mph and at an altitude of 2640 ft. If the plane flies horizontally in a straight line, find the rate at which the dista
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Question 328491: 5. An airplane flies over an observer with a velocity of 400 mph and at an altitude of 2640 ft. If the plane flies horizontally in a straight line, find the rate at which the distance x from the observer to the plane is changing 0.6 min after the plane passes over the observer. RE sketch below.
400 mph P
You can put this solution on YOUR website! There a different ways to go about it, but I am going to convert everything to miles.
Since the plane is traveling 400 mph, in .6 minutes it travels x=4 miles.
We can build a right triangle. Let y=1/2 miles (2640 feet). This remains constant because the plane is not going higher or lower. Thus, dy/dt=0
dx/dt=400 mph
By Pythagoras, the distance from the observer to the plane is the hypoteneuse of the triangle: D= miles.
So, we have
Differentiate implicitly w.r.t time(t).
Enter in the knowns and solve for dD/dt, the rate of change of the distance between the observer and the plane.
mph
