Question

A plane is flying away from you at 16000 mph at a constant altitude of 4 miles. How fast is the planet's distance from you increasing at the moment when the plane is flying over a point on the ground 3 miles from you?

Answer 1

The distance between the plane and the observer is increasing at a rate of 11045 mph when the plane is flying over a point 3 miles from the observer.

Step-by-step explanation:

To solve this problem, we can use the concept of relative velocity. The speed of the plane relative to the observer on the ground is 16000 mph. The distance between the plane and the observer is the hypotenuse of a right triangle with the vertical leg being 4 miles and the horizontal leg being 3 miles. Using the Pythagorean theorem, we can find that the distance is about 5 miles. To find how fast the distance is increasing at the moment when the plane is flying over the point 3 miles from the observer, we can differentiate the distance equation with respect to time and substitute the values.

The rate of change of the distance at that moment is about 11045 mph.