You are on an airplane traveling 30 south of due west at 130

You are on an airplane traveling 30° south of due west at 130 m/s with respect to the air. The air is moving with a speed 49 m/s with respect to the ground due north.

1) What is the speed of the plane with respect to the ground? _____ m/s

2) What is the heading of the plane with respect to the ground? (Let 0° represent due north, 90° represents due easth). _____° East of due North

3) How far west will the plane travel in 1 hour? ____ m

Solution

1.speed of airplane = 130 cos 30 (-i) + 130sin 30(-j)=-112.58 i -65 j

speed of air = 49 j

resultant speed = -112.58 i-65j + 49j = -112.58 i - 16j

= 113.71 m/s

2. angle with west = tan inv( 16/112.58) = 8.08 degree south of west which is 261.91 degree east of due north

3. towards west it will travel = 112.58 x 3600= 405298 m