After one hour in flight, an airplane is located 200 miles north and 300 miles west of the airport. What is the magnitude of the plane's velocity? Round your answer to the nearest mile per hour.

a) 22 miles per hour

b) 128 miles per hour

c )256 miles per hour

d) 361 miles per hour

I don't understand this! Thank you for your help!

the distance gone is

√(200^2+300^2) = 100√13 = 360.55

That was done in 1 hour, so it's also the plane's speed, in mi/hr.

Assuming it started at the airport...

To find the magnitude of the plane's velocity, we need to consider its displacement and the time taken. In this scenario, the displacement is the straight-line distance between the airport and the position of the plane after one hour. We can use the Pythagorean theorem to calculate this displacement:

Displacement = sqrt((200 miles)^2 + (300 miles)^2)

Displacement = sqrt(40000 miles^2 + 90000 miles^2)

Displacement = sqrt(130000 miles^2)

Displacement ≈ 360.5551 miles

Now, to find the magnitude of the plane's velocity, we divide the displacement by the time taken, which is 1 hour in this case:

Magnitude of velocity = Displacement / Time

Magnitude of velocity ≈ 360.5551 miles / 1 hour

Magnitude of velocity ≈ 360.5551 miles per hour

Rounding to the nearest mile per hour gives us an answer of:

Magnitude of velocity ≈ 361 miles per hour

Therefore, the correct option in this case is d) 361 miles per hour.

To find the magnitude of the plane's velocity, we need to calculate the total distance traveled by the plane after one hour. We can use the Pythagorean theorem to find this distance.

Let's consider the northward distance of 200 miles as one side of a right triangle, and the westward distance of 300 miles as the other side. The total distance traveled by the plane is the hypotenuse of this right triangle.

Using the Pythagorean theorem, we can calculate the magnitude of the plane's velocity:

(200^2 + 300^2) = (40000 + 90000) = 130000

Taking the square root of 130000, we get:

sqrt(130000) ≈ 360.56

Rounded to the nearest mile per hour, the magnitude of the plane's velocity after one hour is approximately 361 miles per hour. Therefore, the correct option is:

d) 361 miles per hour