Calculating the Distance Between Two Aircraft

What is the distance between two aircraft after 6 hours?

Calculate the distance between the planes after 6 hours. Give your answer in km, to the nearest km.

Answer:

2392 kilometers

When two aircraft leave an airfield at the same time, traveling due south at 85 m/s and due east at 71 m/s respectively, we can calculate the distance between them after 6 hours by using the Pythagorean theorem. This theorem is applicable since the aircraft are moving at right angles to each other.

First, we calculate the distance traveled by each aircraft in 6 hours:

1. Aircraft traveling south:
   • Distance = Velocity × Time
   • Distance = 85 m/s × (6 hours × 3600 seconds/hour)
   • Distance = 1836000 meters
2. Aircraft traveling east:
   • Distance = Velocity × Time
   • Distance = 71 m/s × (6 hours × 3600 seconds/hour)
   • Distance = 1533600 meters

With the southbound distance of 1836000 meters and eastbound distance of 1533600 meters, applying the Pythagorean theorem gives us the distance between the aircraft:

• Distance = √(southbound distance² + eastbound distance²)
• Distance = √((1836000 m)² + (1533600 m)²)
• Distance ≈ 2391760.78 meters

Converting this distance to kilometers, we get approximately 2391.76 kilometers. Rounding to the nearest kilometer, the distance between the two aircraft after 6 hours is approximately 2392 kilometers.