Final answer:
The final displacement of the F-35B after a vertical takeoff and a 30° angled flight path for 20 km is approximately 20.00 km as calculated using the Pythagorean theorem on the horizontal and vertical components of the displacement.
Step-by-step explanation:
The student's question involves calculating the final displacement of the F-35B Lightning II after a vertical takeoff and subsequent angled flight. To solve for the displacement, we first note the two parts of the jet's motion: a vertical takeoff to 20 m, and then a flight path at a 30° angle for 20 km. For the angled flight path, the horizontal and vertical components must be found using trigonometric functions, specifically the cosine and sine functions respectively.
The horizontal displacement (x) is given by the cosine of the angle times the distance flown: x = cos(30°) × 20 km. The cosine of 30° is √3/2, so x = (√3/2) × 20 km = 17.32 km. The vertical displacement (y) includes the initial 20 m takeoff plus the sine component for the distance flown: y = 20 m + sin(30°) × 20 km. The sine of 30° is 1/2, so y = 20 m + (1/2) × 20 km = 20 m + 10 km. However, we need to convert 20 m to kilometers to combine these values: 20 m = 0.02 km, so y = 0.02 km + 10 km = 10.02 km. The final displacement is the vector sum of these components, which can be found using the Pythagorean theorem: displacement = √(x² + y²).
Plugging in the values, we get displacement = √(17.32 km² + 10.02 km²) which is approximately 20.00 km. Thus, the correct answer is (i) 20.00 km.