Find u middot v exactly where v 100 v 250 pi6 is the angl

Find u middot v exactly where |v| = 100, |v| = 250, = pi/6 is the angle between u and v. A plane is flying a heading of N 69 degree E with airspeed of 225 mph. The wind is blowing at 44 mph $21 degree D. What are its actual heading and groundspeed? Round to one decimal place.

Solution

a) IuI = 100, IvI = 250, angle = pi/6 = 30

Then u + v = sqrt[u^2 + v^2 - 2uvcos30] = sqrt[100^2 + 250^2 - 2*100*250*cos30] = 2540.5