To sketch the diagram, start by drawing the x-y grid and labeling the x-axis as East-West and the y-axis as North-South. The origin (0,0) represents the starting point.
To draw the line representing the jet's velocity relative to the air, start from the origin and draw a horizontal line to the right. Label this line as 425, representing the jet's speed in miles per hour (mph) going East.
From the end of that line, draw a vertical line upwards to represent the wind blowing due North. Label this line as 40, representing the wind's speed in mph blowing North.
Now, join the endpoint of the wind line to the origin to complete the vector diagram. This will form a right-angled triangle, with the hypotenuse representing the magnitude of the resultant velocity of the jet.
To find the direction angle of the plane, you can use the tangent function (tan). The tangent of an angle is equal to the ratio of the opposite side to the adjacent side in a right-angled triangle.
In this case, the angle you want to find is the small angle at the origin. So you need to find the ratio of the vertical side (40) to the horizontal side (425) since tangent is equal to opposite/adjacent.
tan(theta) = 40/425
Solve for theta (angle):
theta = arctan(40/425)
Use a calculator to find arctan(40/425) β 5.383 degrees.
However, it seems you are trying to find the angle clockwise from North. In navigation terms, angles are stated clockwise from North. So to get the angle you need, subtract the obtained angle (5.383 degrees) from 90 degrees:
angle = 90 - 5.383 β 84.617 degrees.
Therefore, the direction of the jet is approximately 84.62 degrees clockwise from North.