Two Airplanes leave an airport at the same time on different runways. One flies on a bearing of N66degreesW at 325 miles per hour. The other airplane flies on a bearing öf S26degreesW at 300 miles per hour. How far apart will the airplanes be after 2 hours?
After you make your sketch, it should be simple to calculate the angle between their flight-paths to be 88° , and after 2 hours the distance covered would be
650 and 600 miles. So a direct application of the cosine law ....
d^2 = 650^2 + 600^2 - 2(650)(600)cos88°
= ...
d = √.....
I get appr 869 miles
Well, the first thing I would suggest is that they should probably stop flying towards each other if they want to stay far apart. Safety first, you know?
But to answer your question, we can use some trigonometry to find the distance between the two airplanes. Let's call the distance traveled by the first airplane A, and the distance traveled by the second airplane B.
Using basic trigonometry, we can find that:
A = 325 * cos(66)
B = 300 * cos(26)
After 2 hours, the distance traveled by the first airplane would be:
Distance_A = A * 2
And the distance traveled by the second airplane would be:
Distance_B = B * 2
To find the distance between the two airplanes, we can use the Pythagorean theorem:
Distance = sqrt((Distance_A)^2 + (Distance_B)^2)
Now, let's calculate all this:
A = 325 * cos(66) = 127.63 miles
B = 300 * cos(26) = 269.1 miles
Distance_A = A * 2 = 255.26 miles
Distance_B = B * 2 = 538.2 miles
Distance = sqrt((Distance_A)^2 + (Distance_B)^2) = sqrt(255.26^2 + 538.2^2) = 591.35 miles
So, the airplanes will be approximately 591.35 miles apart after 2 hours. But remember, it's always better to maintain a safe distance and not fly towards each other!
To find the distance between the two airplanes after 2 hours, we need to calculate the displacement of each airplane in that time.
First, let's calculate the displacement of the first airplane:
Distance = Speed × Time
Distance = 325 miles/hour × 2 hours
Distance = 650 miles
Now, let's calculate the displacement of the second airplane:
Distance = Speed × Time
Distance = 300 miles/hour × 2 hours
Distance = 600 miles
Now, we have the two displacements. To find the distance between the airplanes, we can use the Pythagorean theorem:
Distance^2 = (650 miles)^2 + (600 miles)^2
Calculating the value:
Distance^2 = 422,500 + 360,000
Distance^2 = 782,500
Now, taking the square root of both sides:
Distance = √(782,500)
Distance ≈ 884.71 miles
Therefore, the two airplanes will be approximately 884.71 miles apart after 2 hours.
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.