An airplane travelling north at 400 m/s is accelerated due east at a rate of 50m/s^2 for 6 seconds. If the effects of air resistance and gravity are ignored, what is the final speed of the plane?

Question

My working:
v=vo+at
where a=50m/s
Vo = 400 m/s
t = 6s

thus: Vo=400+50(6)
=700m/s

But the correct answer is 500 m/s what am i doing wrong?

Answer 1

The two numbers cannot be added directly, because they are 90o out of phase:
V = 300 + 400i.
You only want the magnitude:
V = sqrt(300^2+400^2) = 500 m/s.