Resultant Vector of a Helicopter's Flight Path

What is the resultant vector of a helicopter's flight path?

A helicopter rises 200 m then flies 600 m in a straight line parallel to the ground. Determine the resultant vector.

Answer:

The helicopter's resultant vector has a displacement of approximately 632.46 m at an angle of 18.43 degrees above the horizontal, calculated using vector addition, Pythagorean theorem, and trigonometry.

When a helicopter climbs vertically by 200 m and then travels horizontally for 600 m, we can calculate the resultant vector to determine the overall displacement. This involves adding the vertical and horizontal components of the helicopter's motion to find the resultant vector magnitude and direction.

First, we represent the vertical climb as a vector (0, 200 m) and the horizontal flight as a vector (600 m, 0). By applying the Pythagorean theorem, we can find the magnitude of the resultant vector:

Magnitude: R = √(Vx² + Vy²) = √(600² + 200²) = √(360000 + 40000) = √(400000) = 632.46 m (approx)

Next, to determine the angle of the resultant vector, we use trigonometry. The tangent function helps us find the angle above the horizontal:

Angle: θ = arctan(Vy / Vx) = arctan(200 / 600) ≈ 18.43 degrees

Therefore, the helicopter's resultant vector has a displacement of approximately 632.46 m at an angle of 18.43 degrees above the horizontal. This calculation allows us to understand the helicopter's overall motion and trajectory during its flight.