A novice pilot sets a plane's controls, thinking the plane will fly at 2.50 * 2 to the 2nd power km/h to the north. if the wind blows at 75km/h toward the southeast, what will the plane's new resultant velocity be? use graphical techniques.

Are you sure you don't mean the plane's speed is 2.50*10^2 km/h?
2.50*2^2 = 10 km/h is slower than a bicycle, and lot slower than the wind.

Whatever it is, add the two vectors.

1 answer

Draw a vector for the plane's speed, pointing north, with a length of 2.50*10^2 km/h.
Draw a vector for the wind, pointing southeast, with a length of 75 km/h.
The resultant vector is the vector sum of the two vectors.
It will point in the direction of the angle between the two vectors, and have a length equal to the sum of the two lengths.