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
Alright — let's do this. This problem involves vector addition. We need to find the magnitude of the resultant displacement. Step 1: Resolve each displacement into its East (x) and North (y) components. First displacement (D_1): 6.0 m East D_1x = 6.0 m D_1y = 0 m Second displacement (D_2): 10.0 m N30°E This means 30^ East of North. If we consider North as the y-axis and East as the x-axis, the angle with the y-axis is 30^. The East (x) component is D_2 (30^). The North (y) component is D_2 (30^). D_2x = 10.0 m × (30^) = 10.0 m × 0.5 = 5.0 m D_2y = 10.0 m × (30^) = 10.0 m × sqrt(3)2 ≈ 10.0 m × 0.866 = 8.66 m Step 2: Sum the components to find the total displacement components (R_x and R_y). Total East component (R_x): R_x = D_1x + D_2x = 6.0 m + 5.0 m = 11.0 m Total North component (R_y): R_y = D_1y + D_2y = 0 m + 8.66 m = 8.66 m Step 3: Calculate the magnitude of the total displacement (R) using the Pythagorean theorem. R = sqrt(R_x^2 + R_y^2) R = sqrt((11.0 m))^2 + (8.66 m)^2 R = sqrt(121.0 m)^2 + 74.9956 m^2 R = sqrt(195.9956 m)^2 R ≈ 13.9998 m Rounding to one decimal place, R ≈ 14.0 m. Using exact values for (30^) and (30^): D_2x = 10 × (1)/(2) = 5 m D_2y = 10 × sqrt(3)2 = 5sqrt(3) m R_x = 6 + 5 = 11 m R_y = 5sqrt(3) m R = sqrt((11)^2 + (53))^2 R = sqrt(121 + (25 × 3)) R = sqrt(121 + 75) R = sqrt(196) R = 14 m The final answer is D) 14.0 m. Got more? Send 'em!