An airplane undergoes the following displacements: first, it flies 40 km in a direction 30° east of north. next, it flies 56 km due south. finally, it flies 100 km 30° north of west. using analytical methods, determine how far the airplane ends up from its starting point.

Distance from start point is 72.5km

Explanation:

The attached Figure shows the plane trajectories from start point (0,0) to (x1,y1) (d1=40km), then going from (x1,y1) to (x2,y2) (d2=56km), then from (x2,y2) to (x3,y3) (d3=100). Taking into account the angles and triangles formed (shown in the Figure), it can be said:

Using the Pitagoras theorem, the distance from (x3,y3) to the start point can be calculated as:

Replacing the given values in the equations, the distance is calculated.