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
Step 1: Resolve the first displacement into components. The first displacement is 20.0 m east. d_1x = 20.0 m d_1y = 0 m Step 2: Resolve the second displacement into components. The second displacement is 20.0 m at 30^ north of east. d_2x = 20.0 (30^) m d_2y = 20.0 (30^) m Using (30^) = sqrt(3)2 and (30^) = (1)/(2): d_2x = 20.0 (sqrt(3)2) = 10sqrt(3) m ≈ 17.32 m d_2y = 20.0 ((1)/(2)) = 10.0 m Step 3: Sum the x-components and y-components to find the resultant components. R_x = d_1x + d_2x = 20.0 m + 10sqrt(3) m = (20.0 + 10sqrt(3)) m R_x ≈ 20.0 + 17.32 = 37.32 m R_y = d_1y + d_2y = 0 m + 10.0 m = 10.0 m Step 4: Calculate the magnitude of the resultant displacement. The magnitude R is given by the Pythagorean theorem: R = sqrt(R_x^2 + R_y^2) R = sqrt((20.0 + 103))^2 + (10.0)^2 R = sqrt((400 + 4003) + 300) + 100 R = sqrt(800 + 4003) Using sqrt(3) ≈ 1.732: R = sqrt(800 + 400(1.732)) R = sqrt(800 + 692.8) R = sqrt(1492.8) R ≈ 38.637 m Rounding to one decimal place, the magnitude is 38.6 m. Comparing with the given options: A. 28.3 m B. 40.0 m C. 38.6 m D. 10.4 m The closest option is C. The final answer is C. 38.6 m. Send me the next one 📸