you walk west for 52 m, then you walk 33.2° north of west for 44 m, and finally you walk due north for 25 m. Find the components of your final displacement, from your initial to final point, along the north and west directions.
D = -52 + 44[146.8o] + 25i
D = -52 + -36.8 + 24.1i + 25i
D = -88.8 + 49.1i, Q2.
To find the components of your final displacement along the north and west directions, we can break down the given information step by step.
Step 1: Walk west for 52 m
Walking west means moving in the negative x-direction. Therefore, the westward component of your displacement is -52 m in the x-direction.
Step 2: Walk 33.2° north of west for 44 m
To find the northward and westward components of this step, we need to resolve the displacement into its x and y-components. Let's assume the angle is measured counterclockwise from the negative x-axis.
The northward component can be found by using the formula: northward component = displacement * sin(angle)
northward component = 44 m * sin(33.2°)
northward component ≈ 23.331 m
The westward component can be found by using the formula: westward component = displacement * cos(angle)
westward component = 44 m * cos(33.2°)
westward component ≈ 36.450 m
Step 3: Walk due north for 25 m
Walking due north means moving in the positive y-direction. Therefore, the northward component of your displacement is +25 m in the y-direction, while the westward component remains 0, as there is no motion in the westward direction.
Final Displacement:
To find the final displacement, you need to add up the individual components.
The northward component of the final displacement is: +23.331 m (from Step 2) + 25 m (from Step 3) = 48.331 m north
The westward component of the final displacement is: -52 m (from Step 1) + 36.450 m (from Step 2) = -15.550 m west
Therefore, the components of your final displacement along the north and west directions are 48.331 m north and -15.550 m west, respectively.