Calculating Plane Displacement: A Trigonometry Challenge
How to find the distance of a plane from its starting point given its speed, time, and direction?
The plane flies hours at mph on a bearing of. It then turns and flies hours at the same speed on a bearing of. How far is the plane from its starting point?
Calculating the Displacement of a Plane
To determine the distance of the plane from its starting point, we need to apply the Law of Cosines to calculate the displacement. The displacement is essentially the third side of a triangle formed by the two paths taken by the plane.
When dealing with vectors and trigonometry in this scenario, the Law of Cosines is a fundamental tool. By knowing the speed of the plane and the time it traveled on each path, we can calculate the displacement through the following formula:
c² = a² + b² - 2abcos(θ)
Where:
- c represents the displacement (distance between the starting and ending points).
- a and b are the distances traveled in the first and second paths, calculated as speed multiplied by time.
- θ is the angle between the two paths.
Without the specific values for time, speed, and angles, we cannot determine the exact distance of the plane. It is important to provide complete data for accurate calculations in such problems.