Answer:
Please find attached the motion of the helicopter (drawn to scale) showing the magnitude and the direction of the net displacement of the helicopter obtained by measurement to be 105 miles and 19° respectively
By calculation, the magnitude of the net displacement is approximately 105.83 miles and the direction of the net displacement is approximately 19.1066°
Step-by-step explanation:
The parameters of the motion of the helicopter are;
The distance the helicopter flies before turning = 80 miles
The distance the helicopter then turns and flies = 40 miles
The direction the helicopter turns = 60°
Therefore, we have;
The total length the helicopter flies in the original direction = The component of the length of the 40 mile flight that is in the original direction + The distance the helicopter flies before turning
∴ The total length the helicopter flies in the original direction = 40 × cos(60°) + 80 = 20 + 80 = 100
The total length the helicopter flies in the original direction = 100 miles
The component of the 40 mile flight that is perpendicular to the original direction = 40 × sin(60°) = 40 × √3/2
The magnitude of the net displacement = √(100² + (40×√3/2)²) ≈ 105.83
The magnitude of the net displacement ≈ 105.83 miles
The direction of the net displacement = tan⁻¹((40 ×√3/2)/(100)) ≈ 19.1066°
The direction of the net displacement ≈ 19.1066°.