9. an airplane flies 1512.0 km w 19.30° n from toronto to winnipeg, continues 571.0 km w 4.35° n from…

Explanation:

Step1: Resolve vectors into components

For the first - leg: The west - east component $x_1=- 1512.0\cos(19.30^{\circ})\approx - 1429.77$ km (negative because it is west - ward) The north - south component $y_1 = 1512.0\sin(19.30^{\circ})\approx500.97$ km For the second - leg: The west - east component $x_2=-571.0\cos(4.35^{\circ})\approx - 569.37$ km The north - south component $y_2 = 571.0\sin(4.35^{\circ})\approx43.17$ km For the third - leg: The west - east component $x_3=-253.1\cos(39.39^{\circ})\approx - 194.97$ km The north - south component $y_3 = 253.1\sin(39.39^{\circ})\approx160.17$ km

Step2: Sum up the x - components

$x=x_1 + x_2+x_3=-1429.77-569.37 - 194.97=-2194.11$ km

Step3: Sum up the y - components

$y=y_1 + y_2+y_3=500.97 + 43.17+160.17=704.31$ km

Step4: Calculate the magnitude of the total displacement

The magnitude of the displacement $d=\sqrt{x^{2}+y^{2}}=\sqrt{(-2194.11)^{2}+704.31^{2}}\approx2304.3$ km

Step5: Calculate the direction of the total displacement

The direction $\theta=\tan^{-1}\left(\frac{y}{x}\right)=\tan^{-1}\left(\frac{704.31}{-2194.11}\right)+180^{\circ}\approx162.2^{\circ}$ counter - clockwise from the positive x - axis or $N(90^{\circ}-(180^{\circ}-\theta))W=N17.8^{\circ}W$

Answer:

The total displacement of the plane is approximately $2304.3$ km in the direction of $N17.8^{\circ}W$