What is the rate at which the distance between two airplanes is changing while they are both flying towards the same airport?

Question

Cordelia · Answer

The rate at which the distance between the airplanes is changing is 1,210,241 km/h.       Explanation:     Given Data:     Airplane A is flying east at 795 km/h     Airplane B is flying north at 754 km/h     The airport is located 66 kilometers east of Airplane A and 71 kilometers north of Airplane B     We need to find the rate at which the distance between the airplanes is changing as they fly towards the same airport.      Solution:     To find the rate of change in the distance between the two airplanes, we can use the Pythagorean theorem because the distance between them forms a right triangle.          Let the distance between the airplanes be d(t), where t is time.     Using the Pythagorean theorem, we have:     d(t)^2 = (66)^2 + (71)^2     d(t) = sqrt((66)^2 + (71)^2)          To find the rate at which d(t) is changing, we use the chain rule of differentiation:     d(d(t))/dt = (dx(t)/dt) * (dx(t)/dt) + (dy(t)/dt) * (dy(t)/dt)     where dx(t)/dt is the rate of change of the x-coordinate, and dy(t)/dt is the rate of change of the y-coordinate.          Substituting the given speeds for each airplane:     d(d(t))/dt = (795)^2 + (754)^2     d(d(t))/dt = 1,210,241 km/h      Therefore, the rate at which the distance between the airplanes is changing is 1,210,241 km/h.

Calculating the Rate of Change Between Two Airplanes Flying Towards the Same Airport

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