You are on an airplane traveling 30degree south of due west

You are on an airplane traveling 30degree south of due west at 100 m/s with respect to the air. The air is moving with a speed 37 m/s with respect to the ground due north. What is the speed of the plane with respect to the ground? 2) What is the heading of the plane with respect to the ground? (Let 0degree represent due north, 90degree represents due easth). degree East of due North 3) How far west will the plane travel in 1 hour? m

Solution

let velocity of airplane be v 1 velocity of air = v2 and velocity of ground = v3

now velocity of airplane with respect to air = v12 = 100 cos 30 (-i) + 100 sin 30 (-j)

or v12 = -86.6 i - 50 j

velocity of air with respect to ground = 37 j

velocity of airc raft with respect to ground =velocity of airplane with respect to air +velocity of air with respect to ground = -86.6 i - 13 j

therefore speed = 87.57 m/s

2) angle about negative y axis = tan^-186.6/13 =81.46 degree

therefore due east of north = 180 + 81.46 = 261.46 degree

3) the speed along the west is 86.6 m/s

therefore distance travelled in 1 hr = 86.6 x 3600 /1000 = 311.76 km