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 the solution for the lady's displacement: Step 1: Identify the individual displacement vectors. The lady walks 1 km due East. Let this be D_1. The lady then walks 1 km due North. Let this be D_2. Step 2: Represent the displacements in component form. Let East be the positive x-direction and North be the positive y-direction. D_1 = 1i + 0j km D_2 = 0i + 1j km Step 3: Calculate the total displacement vector. The total displacement D_total is the sum of the individual displacements: D_total = D_1 + D_2 D_total = (1+0)i + (0+1)j km D_total = 1i + 1j km Step 4: Calculate the magnitude of the total displacement. The magnitude of the total displacement is found using the Pythagorean theorem: |D_total| = sqrt((1 km))^2 + (1 km)^2 |D_total| = sqrt(1 + 1) km |D_total| = sqrt(2) km |D_total| ≈ 1.414 km Step 5: Calculate the direction of the total displacement. The direction is found using the arctangent function: = (North componentEast component) = (1 km1 km) = (1) = 45^ Since both components are positive, the direction is 45^ North of East. The lady's displacement is 1.414 km at 45^ North of East. That's 2 down. 3 left today — send the next one.