Answer:
The resultant speed = 181.3 mph
The final direction = 38.7° northeast.
Step-by-step explanation:
We need to find the component in the x-direction and in the y-direction of the speed:
For the plane:
[tex] v_{p_{x}} = 200cos(45) = 141.42 [/tex]
[tex] v_{p_{y}} = 200sin(45) = 141.42 [/tex]
For the wind we have:
[tex] v_{w_{x}} = -28 [/tex]
[tex] v_{w_{y}} = 0 [/tex]
Now, the total speed in the x-direction and in the y-direction is:
[tex] V_{x} = v_{p_{x}} + v_{w_{x}} = 141.42 - 28 = 113.42 [/tex]
[tex] V_{y} = v_{p_{y}} + v_{w_{y}} = 141.42 [/tex]
Hence, the resultant speed is:
[tex] V = \sqrt{V_{x}^{2} + V_{y}^{2}} = \sqrt{(113.42)^{2} + (141.42)^{2}} = 181.3 mph [/tex]
Finally, the direction of the plane is:
[tex] tan(\theta) = \frac{V_{y}}{V_{x}} = \frac{141.42}{113.42} = 1.25 [/tex]
[tex] \theta = 51.3 ^{\circ} [/tex]
[tex] \theta = 90 - 51.3 = 38.7 ^{\circ} [/tex]
The plane is moving at 38.7° northeast.
I hope it helps you!
