Final answer:
To find the ground velocity of the airplane, subtract the wind velocity from the airspeed and calculate the magnitude and direction of the resultant velocity using vector addition.
Step-by-step explanation:
To find the ground velocity of the airplane, we need to calculate its resultant velocity by considering the effect of the wind. We can use vector addition to find the resultant velocity. The wind is blowing from the east at 87 km/h, which is opposite to the heading of the airplane. If we subtract the wind velocity from the airplane's airspeed, we can find the resultant velocity. Using the formula for vector addition, we can calculate the magnitude and direction of the resultant velocity. The magnitude of the resultant velocity is calculated as the square root of the sum of the squares of the horizontal and vertical components of the velocity. In this case, the horizontal component is (-750 km/h + 87 km/h) = -663 km/h, and the vertical component is 0 km/h. Therefore, the magnitude of the resultant velocity is sqrt((-663)^2 + 0^2) = 663 km/h. The direction of the resultant velocity can be calculated using the inverse tangent function. The angle can be found by taking the inverse tangent of the vertical component divided by the horizontal component. In this case, the angle is tan^(-1)(0 / (-663)) = 0°. Therefore, the direction of flight is 0°.