Physics help please!!! Best answer 10 pts?

Question

A pilot wishes to fly due south. Wind of 25km/h blowing to west. Flying speed in still air is 300km/h. What direction should pilot head in?

Please show work and answer

Answer 1

its hard to show by just typing you have to use trig and head the plane the opposite direction of the wind which will force you over into a straight line (due south) you need to used right hand trig.

the answer should be 4.78 degrees east of south i might be wrong tho forgot a bit over the summer :)

Answer 2

just do arctan(25/300)

its 4.764degrees, and it would be east of south.

make it a good day

Answer 3

It's not arctan(25/300) it's arcsin(25/300) = 4.78 degrees east of south.  It's only a small difference because the angle is so small anyway, but may as well be correct.

As to why, it's a problem of vector addition:

v_pg = velocity of plane relative to ground (due south)

v_pw = velocity of plane relative to wind (angle to be determined, magnitude 300)

v_wg = velocity of wind relative to ground (due west, magnitude 25)

v_pg = v_pw + v_wg, so the vectors form a right triangle with the unknown vector v_pw as the hypoteneuse and v_wg as the side opposite the unknown angle.  sin = opposite / hpoteneuse, hence you need to use the arcsin to find the unknown angle.

Needless to say a picture makes this easier to grasp, try illustrating the above description.