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

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

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.

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