Straight-line Distance and Direction Calculation of a Small Plane

What is the straight-line distance from the starting point of the small plane?

1. 61.6 km

2. 50.0 km

3. 70.0 km

What is the direction of the straight-line path to the final position of the small plane?

1. 30° counterclockwise from the east axis

2. 45° clockwise from the east axis

3. 60° counterclockwise from the east axis

Solution:

The plane's straight-line distance from the starting point is approximately 61.6 km, and the direction of the straight-line path to the final position is approximately 30° counterclockwise from the east axis.

To find the plane's straight-line distance and direction, we can use vector addition. Let's represent the first leg of the plane's journey as vector A and the second leg as vector B.

Vector A has a magnitude of 35.0 km and a direction of 50° north of east. We can represent it graphically by drawing an arrow pointing in the direction 50° north of east with a length of 35.0 units.

Vector B has a magnitude of 31.0 km and a direction of 20° north of east. We can represent it graphically by drawing an arrow pointing in the direction 20° north of east with a length of 31.0 units.

To add these vectors, we place the tail of vector B at the head of vector A. The resultant vector, which represents the straight-line distance and direction, is the vector from the tail of vector A to the head of vector B.

Using the graphical method, we can measure the magnitude of the resultant vector to find the straight-line distance from the starting point. We can also measure the angle counterclockwise from the east axis to determine the direction of the straight-line path to the final position.