Need help on a vector math word problem.

Question

A hot air balloon is flying at a constant speed of 20 mi/h at a bearing of N 36 degrees E. There is a 10 mi/h cross wind blowing due east. What is the balloon's actual speed and direction? Round angles to the nearest degree and other values to the nearest tenth.

Answer 1

v = {[(20sin36°)i + (20cos36°)j] + 10i} mi/h

 

v_E = 20sin36º + 10 = 21.76 mi/h

 

v_N = 20cos36° = 16.18 mi/h

 

v = √(v_E² + v_N²) = √(21.76² + 16.18²) mi/h = 27.12 mi/h

 

θ = tan^-1(v_N/v_E) = tan^-1(16.18/21.76) = 36.6º north of east