A plane flies 300 km north and then 400 km east. What is the angle of the result

A plane flies 300 km north and then 400 km east. What is the angle of the resultant displacement with respect to the north?

A plane flies 300 km north and then 400 km east. What is the angle of the resultant displacement with respect to the north?

Step 1: Understand the problem. A plane flies 300 km north and then 400 km east.
Step 2: Visualize the path. Imagine a right triangle where one side (north) is 300 km and the other side (east) is 400 km.
Step 3: Identify the angle we need to find. We want the angle between the north direction and the line from the starting point to the endpoint (resultant displacement).
Step 4: Use the tangent function. The tangent of the angle (let's call it θ) is the opposite side (east) over the adjacent side (north). So, tan(θ) = opposite/adjacent = 400/300.
Step 5: Calculate the tangent ratio. This gives us tan(θ) = 400/300.
Step 6: Use the inverse tangent function to find the angle. θ = tan^(-1)(400/300).
Step 7: Calculate the angle using a calculator. This gives us θ ≈ 53.13 degrees.

Vector Addition – Understanding how to combine two displacement vectors to find the resultant vector.
Trigonometry – Using the tangent function to find angles in right triangles formed by the displacement vectors.
Coordinate System – Recognizing the north and east directions in a Cartesian coordinate system.