An airplane has a speed 590 km/h . If a wind begins blowing from the southwest at a speed of 94.9 km/h (average). In what direction should the pilot aim the plane so that it will fly due south?

The pilot should aim the airplane towards the southeast direction to fly due south. Explanation: The airplane's speed is 590 km/h, and the wind is blowing from the southwest at a speed of 94.9 km/h. To determine the direction the pilot should aim the plane, we need to calculate the resultant vector of the airplane's speed and the wind's speed. This can be done using vector addition. We can use the Pythagorean theorem and trigonometry to calculate the magnitude and direction of the resultant vector. The magnitude of the resultant vector is given by: resultant speed = ?(airplane speed^2 + wind speed^2) resultant speed = ?(590^2 + 94.9^2) = 596.9 km/h The direction of the resultant vector can be determined using trigonometry. We can use the inverse tangent function to find the angle between the direction of the airplane's speed and the wind's direction: ? = tan^-1(wind speed / airplane speed) ? = tan^-1(94.9 / 590) = 8.8 degrees Therefore, the pilot should aim the airplane towards the southeast direction (8.8 degrees east of due south) to counteract the effect of the wind and fly due south.