Choose the correct answer.
Speed of Plane A = 450 mph.
Speed of Plane B = 350 mph.
Both planes leave from Kansas City at the same time.
Plane A flies due West.
Plane B flies due South.
After 2.5 hours, how far is Plane A from Plane B? $\square$ miles.
Answer (1)
Calculate the distance Plane A travels: d i s t an c e A = 450 mph × 2.5 hours = 1125 miles .
Calculate the distance Plane B travels: d i s t an c e B = 350 mph × 2.5 hours = 875 miles .
Apply the Pythagorean theorem to find the distance between the planes: d i s t an ce = ( 1125 ) 2 + ( 875 ) 2 .
The distance between Plane A and Plane B is approximately: 1425.22 miles .
Explanation
Calculate individual distances First, we need to determine the distances traveled by each plane. Plane A travels at 450 mph for 2.5 hours, and Plane B travels at 350 mph for the same duration.
Compute distances Let's calculate the distance traveled by Plane A: d i s t an c e A = s p ee d A × t im e = 450 mph × 2.5 hours = 1125 miles Now, let's calculate the distance traveled by Plane B: d i s t an c e B = s p ee d B × t im e = 350 mph × 2.5 hours = 875 miles
Apply Pythagorean theorem Since Plane A flies due West and Plane B flies due South, their paths are perpendicular to each other. This forms a right triangle, where the distance between the planes is the hypotenuse, and the distances traveled by each plane are the legs of the triangle. We can use the Pythagorean theorem to find the distance between the planes.
Calculate the distance The Pythagorean theorem states that a 2 + b 2 = c 2 , where a and b are the lengths of the legs of a right triangle, and c is the length of the hypotenuse. In this case, a = d i s t an c e A = 1125 miles, b = d i s t an c e B = 875 miles, and c is the distance between the planes. d i s t an ce = d i s t an c e A 2 + d i s t an c e B 2 = ( 1125 ) 2 + ( 875 ) 2 d i s t an ce = 1265625 + 765625 = 2031250 ≈ 1425.22 miles
State the final answer Therefore, after 2.5 hours, the distance between Plane A and Plane B is approximately 1425.22 miles.
Examples
This problem demonstrates how navigation and distance calculations are crucial in aviation. Pilots and air traffic controllers use these principles to ensure safe separation between aircraft. For example, understanding the relative positions and speeds of planes helps prevent collisions and maintain organized flight paths, especially in busy airspaces.
