Question

Two commercial airplanes are flying at an altitude of 40,000ft along straight-line courses that intersect at right angles. Plane A is approaching the intersection point at a speed of 429 knots (nautical miles per hour; a nautical mile is 2000 yd or 6000 ft.) Plane B is approaching the intersection at 460 knots. At what rate is the distance between the planes decreasing when Plane A is 2 nautical miles from the intersection point and Plane B is 6 nautical miles from the intersection point?

Answer 1

To find the rate at which the distance between two planes is decreasing, we need to use the concept of relative velocity and the Pythagorean theorem.

Step-by-step explanation:

To find the rate at which the distance between the planes is decreasing, we need to use the concept of relative velocity. We can consider Plane A as the reference point and calculate the velocity of Plane B with respect to A. When Plane A is 2 nautical miles from the intersection point, the distance between Plane A and the intersection point is 2 nautical miles. Similarly, when Plane B is 6 nautical miles from the intersection point, the distance between Plane B and the intersection point is 6 nautical miles. Using the Pythagorean theorem, we can calculate the distance between the two planes. Then, by differentiating this distance with respect to time, we can find the rate at which the distance is decreasing.