How to Calculate the Straight-Line Distance of a Plane Using the Analytical Method

What is the straight-line distance of a plane that flies 37.0 km in a direction 60° north of east and then flies 23.0 km in a direction 25° north of east?

How can we use the analytical method to find the plane's straight-line distance from the starting point?

Solution:

The plane's straight-line distance from the starting point is approximately 20.9 km. To find this distance, we need to break down the plane's motion into its horizontal and vertical components.

Explanation:

First, let's analyze the horizontal component of the plane's motion. When the plane flies 37.0 km in a direction 60° north of east, we can use trigonometry to determine the horizontal displacement. By applying the cosine function, we find that the horizontal component is approximately 18.5 km.

Next, we need to consider the vertical component of the plane's motion. When the plane flies 23.0 km in a direction 25° north of east, we can use the sine function to calculate the vertical displacement. The vertical component is approximately 9.8 km.

Now, to determine the resultant displacement or straight-line distance of the plane from the starting point, we use the Pythagorean theorem. By taking the square root of the sum of the squares of the horizontal and vertical components, we find that the plane's straight-line distance is approximately 20.9 km.

Therefore, by applying the analytical method and trigonometric functions, we can accurately calculate the straight-line distance of a plane's motion from its starting point. This method allows us to understand the spatial position of the plane in a two-dimensional plane.