Question

Suppose an airplane is flying in air with a speed of u=100m/s . The wind is from the south west with a velocity of v= 70m/s

what direction should the airplane head in order to fly directly north ( with respect to the ground)? Give the angle in degrees of west of north

what is the plane's speed as measured by a bystander on the ground

Answer 1

A is heading angle west of north

Wind is taking us NE at 70

North speed over ground = 100 cos A + 70 cos 45

West speed over ground = 100 sin A - 70 cos 45

if we are making a course made good of north, west speed is 0
so
sin A = (70 /100)cos 45
A = 29.7 degrees west of North

Now for speed made good north calculate
100 cos 29.7 + 70 sin 45

Answer 2

by the way I unintentionally used the fact the sin 45 = cos 45 = sqrt2/2

Answer 3

where did the 45 come from ?

Answer 4

wind is from SW
That means it is pushing you NE
NE is 45 degrees east of north (halfway between north which is 0 and east which is 90)
DRAW THE PICTURE !!!!