If an airplane travels at 300 mph with no air resistance,

and it travels directly south with a wind of 50 mph east, how fast is the plane going?

what is √(300^2 + 50^2 ) ?

304.1 correct, so .....

To determine the speed of the plane, we need to consider the vector addition of the airplane's speed and the wind's speed.

The airplane is traveling at a speed of 300 mph directly south, which can be represented as a vector pointing in the south direction with a magnitude of 300 mph.

The wind is blowing with a speed of 50 mph to the east, which can be represented as a vector pointing in the east direction with a magnitude of 50 mph.

To find the resultant vector, we need to combine these two vectors by adding them together using vector addition.

Since the airplane is traveling south and the wind is blowing east, the two vectors are at right angles to each other. We can use the Pythagorean theorem to find the magnitude of the resultant vector (speed of the plane), and we can use trigonometry to find the direction it is traveling.

Let's calculate the speed of the plane using the Pythagorean theorem:

Speed of plane = √(south^2 + east^2)
= √(300^2 + 50^2)
= √(90000 + 2500)
= √92500
≈ 304.14 mph

Therefore, the plane's speed, considering both its original speed and the wind's speed, is approximately 304.14 mph.