To find how far apart the airplanes will be after 2 hours, we need to calculate the distance each airplane has traveled in that time.
Let's start by finding the distance traveled by the first airplane, which flies on a bearing of N66degreesW at 325 miles per hour. Since it's flying for 2 hours at a constant speed, we can calculate its distance using the formula: distance = speed × time.
The distance traveled by the first airplane in 2 hours is:
Distance1 = 325 miles/hour × 2 hours = 650 miles.
Next, let's calculate the distance traveled by the second airplane, which flies on a bearing of S26degreesW at 300 miles per hour. Applying the same formula, we have:
Distance2 = 300 miles/hour × 2 hours = 600 miles.
Now, we have the distances traveled by both airplanes in 2 hours. To find the distance between them, we can use the concept of vector addition.
Since the two airplane paths form a right triangle, we can use the Pythagorean theorem to find the distance between them. The theorem states that the square of the hypotenuse (the distance between the airplanes) is equal to the sum of the squares of the other two sides (distances traveled by each airplane).
Using the Pythagorean theorem:
Distance between airplanes = √(Distance1² + Distance2²)
= √(650² + 600²)
≈ √(422,500 + 360,000)
≈ √782,500
≈ 884.1 miles.
Therefore, the two airplanes will be approximately 884.1 miles apart after 2 hours.