This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.
ScanSolve AI Answer
Here's how to solve this navigation problem: 1) Find its distance from the starting point Step 1: Calculate the distance and North/East components for the first leg. The aircraft flies at 20 km/hr for 3 hours on a bearing of 052°. Distance (d₁) = Speed × Time d₁ = 20 km/hr × 3 hr = 60 km North component (y₁) = d₁ × cos(Bearing) y₁ = 60 km × cos(52°) y₁ ≈ 60 km × 0.6157 = 36.942 km East component (x₁) = d₁ × sin(Bearing) x₁ = 60 km × sin(52°) x₁ ≈ 60 km × 0.7880 = 47.280 km Step 2: Calculate the distance and North/East components for the second leg. The aircraft flies at 30 km/hr for 1.5 hours on a bearing of 028°. Distance (d₂) = Speed × Time d₂ = 30 km/hr × 1.5 hr = 45 km North component (y₂) = d₂ × cos(Bearing) y₂ = 45 km × cos(28°) y₂ ≈ 45 km × 0.8829 = 39.7305 km East component (x₂) = d₂ × sin(Bearing) x₂ = 45 km × sin(28°) x₂ ≈ 45 km × 0.4695 = 21.1275 km Step 3: Calculate the total North and East displacements from the starting point. Total North displacement (Y) = y₁ + y₂ Y = 36.942 km + 39.7305 km = 76.6725 km Total East displacement (X) = x₁ + x₂ X = 47.280 km + 21.1275 km = 68.4075 km Step 4: Calculate the total distance from the starting point using the Pythagorean theorem. Distance = √(X² + Y²) Distance = √((68.4075 km)² + (76.6725 km)²) Distance = √(4679.58 km² + 5878.68 km²) Distance = √(10558.26 km²) Distance ≈ 102.75 km 2) The bearing of the aircraft from the airstrip Step 5: Calculate the bearing of the aircraft from the airstrip. Since both X (East) and Y (North) components are positive, the aircraft is in the North-East quadrant. The bearing is the angle measured clockwise from North. Angle (θ) = arctan(East component / North component) θ = arctan(X / Y) θ = arctan(68.4075 / 76.6725) θ = arctan(0.8921) θ ≈ 41.72° The bearing is written with three digits. Bearing = 041.7° What's next? 📸