SOLUTION: An airplane is flying at 340 km/hr at 12 degrees of East of North. The wind is blowing 40 km/hr at 34 degrees South of East. What is the planes actual velocity?

Question 1204113: An airplane is flying at 340 km/hr at 12 degrees of East of North. The wind is blowing 40 km/hr at 34 degrees South of East. What is the planes actual velocity?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
12 degrees east of north is the same direction as 78 degrees north of east.
the 78 degrees is equal to 90 minus 12.

here's a sketch of the plane's and the wind's velocity.
the sketch is not true to scale.

the length of y1 = 332.870184 in a northerly direction.
the length of y2 = 71.531666 in a southerly direction.
the length of y3 = y1 minus y2 = 310.2 in a northerly direction.

the length of x1 = 70.69 in an easterly direction.
the length of x2 = 33.16 in an easterly direction.
the length of x3 = x1 + x2 = 103.85 in an easterly direction.

the length of h3 = sqrt(310.2^2 + 103.85^2) = 327.12.

the angle of the triangle formed by x3 and y3 and h3 = arcsin(y3/h3) = 71.49 degrees north of east.

the answer to your question is that the plane's actual velocity is given by h3 = 327.12 kilometers per hour.

i did the calculations again with unrounded numbers stored in my calculator and then rounded at the end and got the same answer, so it looks good math wise.

the procedure was to sum up the x1 and x2 components to get the x3 component and to sum up the y1 and y2 components (the y2 component was negative) to get the y3 components, and to use the x3 and y3 components to get the h3 value.

i believe the procedure is sound and has hopefully provided you with the solution you require.

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