Question

50 PTS!!!

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?


1,322


1,258.5


1,425

miles.

Answer 1

Answer: 1425 miles

Explanation:

The distance traveled by Plane A in 2.5 hours is calculated as:

Distance A = Speed A * Time = 450 mph * 2.5 hours = 1125 miles

The distance traveled by Plane B in 2.5 hours is calculated as:

Distance B = Speed B * Time = 350 mph * 2.5 hours = 875 miles

Now, using the Pythagorean theorem, we can calculate the distance between Plane A and Plane B:

Distance AB = √(Distance_A^2 + Distance_B^2)

Distance AB = √(1125^2 + 875^2)

Distance AB = √(1,265,625 + 765,625)

Distance AB = √2,031,250

Distance AB ≈ 1,425 miles

Therefore, after 2.5 hours, Plane A is approximately 1,425 miles away from Plane B.

Answer 2

To determine the distance between Plane A and Plane B after 2.5 hours, we can use the concept of relative velocity. Since Plane A is flying due west and Plane B is flying due south, their velocities are perpendicular to each other.

To calculate the distance between them, we can use the Pythagorean theorem:

Distance =
`√(PlaneA^2 +PlaneB^2)`

First, we calculate the distance flown by Plane A:

Distance flown by Plane A = Speed of Plane A * Time =
`(450mph)(2.5h)=1125miles`

Next, we calculate the distance flown by Plane B:

Distance flown by Plane B = Speed of Plane B * Time =
`(350mph)(2.5) = 875 miles`

Now, we can calculate the distance between Plane A and Plane B using the Pythagorean theorem:

Distance =
`√(1125^2+875^2)`

Distance =
`√(1,265,625 + 765,625)`

Distance =
`√(2,031,250)`

Distance ≈ 1,425 miles

Answer: Therefore, the correct answer is: 1,425 miles.