Question

Our superhero finds himself flying in a strong wind storm. The wind is blowing at 50m/s from

the NW. He sees someone who needs helps that is 200m due north of him. Our hero knows

that he flies at a maximum of 93m/s.

a) In what direction does our hero need to point himself so that he flies due north to

save the person?

b) How long does it take him to get to the person?

Answer 1

Let eastward direction be positive x and northward direction be positive y.

Wind is blowing at 50 m/s from north-west. So, wind velocity=50cos45 -50 sin45

Let the superhero travel at angle from the x axis. So, superhero's velocity=93cos+93 sin

So,net velocity of superhero=(50cos45+93cos)+(93 sin-50 sin45)

Net velocity of superhero must be towards north. So, x component of net velocity must be zero. So,50cos45+93cos=0

=>cos=-(50cos45)/93=0.38=>=cos^-1(-0.38)=112.33 degrees.

So, superhero must travel 112.33 degrees counterclockwise from east direction.

b)if =112.33 deg, net velocity of superhero=93 sin(112.33) - 50 sin45=50.67 m/s

Time=distance/speed=200/50.67=3.95 seconds.