Question

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.

Answer 1

Answer:

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:

$x1=d1*cos(60), y1=d1*sin(60)\\\\ x2=x1 , y2=y1-d2\\\\ x3=x2-d3*cos(30) , y3=y2+d3*sin(30)$

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

$d=\sqrt{x3^{2} +y3^{2} }$

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