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.