A car accelerates at 5 m/s^2 at an angle of 45 degrees north of east. What is the car's acceleration due north?

Answer 1

Draw a little triangle from the origin with the hypotenuse of length 5 and angle 45 degrees above x axis (which by convention points East). The component of acceleration to the North is the opposite side, so sine 45 = y/5, y = 5/sqrt(2) = 3.54 m/s^2 approximately.