Answer:
magnitude = 304.14 km/h
direction: [tex]9.46^o[/tex] West of North
Explanation:
The final plane's vector velocity will be the result of the vector addition of one pointing North of length 300 km/h, another one pointing West of length 50 km/h.
To find the magnitude of the final velocity vector (speed) we need to apply the Pythagorean theorem in a right angle triangle with sides: 300 and 50, and find its hypotenuse:
[tex]|v|=\sqrt{300^2+50^2}=\sqrt{92500} = 304.14[/tex] km/h
The actual direction of the plane is calculated using trigonometry, in particular with the arctan function, since the tangent of the angle can be written as:
[tex]tan(\theta)=\frac{50}{300} = \frac{1}{6} \\\theta = arctan(\frac{1}{6} ) = 9.46^o[/tex]
So the resultant velocity vector of the plane has magnitude = 304.14 km/h,
and it points [tex]9.46^o[/tex] West of the North direction.
