Calculus  URGENT EXAM
posted by Santha .
I HAVE AN EXAM REVIEW QUESTION AND I REALLY NEED HELP.
An airplane has an air speed of 330km/h and is heading in a direction of N30E when it encounters a wind from the north. The resultant ground velocity has a direction of N40E. How long does it take for the plane to travel 960km.

Did you make a diagram?
My vector diagram has angles 10°, 30°, and 140° with the longest sides as 330.
so the side across the 30° represents the ground velocity of the plane, let it be x
By the sine law
x/sin30 = 330/sin140
x = 256.69
so the actual groundspeed is 269.69 km/h, then to go 960 km would take
960/269.69 hours or 3.74 hours
or 3 hours and 44 minutes and 23.5 seconds