4. A plane traveled due south for 200 mi then 180 mi 20° N of W and finally 50 mi due 40° due N of E. Determine the planes total displacement. Draw what is given.
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5. Given the following vectors:
A = 5m, 37° N OF W B. 4m 30° S of E C. 5m 400
N of E D. 10 m North E. 8m East. Find the resultant vector.Draw what is given.
(Draw what is given of 4 and 5. Vector of component method. PLEASE answer with no funny business thankkk you!)
Answer (1)
Step 1: Represent each movement as a vector:A: 200 mi due South → (0, –200)B: 180 mi 20° North of Westx = –180 × cos(20°) ≈ –169.2y = 180 × sin(20°) ≈ 61.5C: 50 mi 40° North of Eastx = 50 × cos(40°) ≈ 38.3y = 50 × sin(40°) ≈ 32.1Step 2: Add all vectors:Total x = –169.2 + 38.3 = –130.9 miTotal y = –200 + 61.5 + 32.1 = –106.4 miStep 3: Displacement = √(x² + y²)= √(130.9² + 106.4²) ≈ √(17134.8 + 11320.96) = √28455.76 ≈ 168.6 miDirection (θ):θ = tan⁻¹(106.4 / 130.9) ≈ 39.5° South of WestFinal Answer 168.6 mi, 39.5° S of W
