A helicopter flies 30 km 30 degrees north of east, drops of the supplies to a research team; it then heads 50 degrees north of west traveling 70 km to drop the supplies to a filming crew. What is the resultant displacement of the helicopter?

D = 71.20 km

Explanation:

In this case, let's get the exercise by parts.

Part 1 would be the first displacement which is 30 km. However, it's displacing north to east 30°, so in this case, if we trace a line of this, it should be a diagonal. So we need to get the value of this displacement in the x and y axis.

Dx1 = 30 cos 30° = 25.98 km

Dy1 = 30 sin 30° = 15 km

Doing the same thing but in the second travel we have:

Dx2 = 70 cos 50° = 45 km

Dy2 = 70 sin 50° = 53.62 km

Now we need to know how was the displacement in both axis. In travel 2, the plane is moving north to west, so, in the x axis, is moving in the opposite direction, therefore:

Dx = - 45 + 25.98 = - 19.02 km

In the y axis, is moving upward so:

Dy = 53.62 + 15 = 68.62 km

Finally to get the resultant displacement:

D = √Dx² + Dy²

Replacing:

D = √ (-19.02) ² + (68.62) ²

D = √5070.46

D = 71.20 km