Question

The 1st leg of my trip I walk da-105 m at a-25° south of east. The 2nd leg of my trip ! dB-125 m at h-15° north of east. On my final leg I walk dc-95 m at θc 61.5° north of west. Choose the coordinate sys so that x is directed towards the east, and v is directed towards the north

(a) Write an expression for the x-component of the final displacement in terms of the given quantities

Answer 1

The x-component of the final displacement is x=−105cos(25°)+125cos(15°)−95cos(61.5°).

The x-component of the final displacement is determined by summing the individual x-components of each leg of the trip. In the chosen coordinate system where x is directed towards the east, and y is directed towards the north, the expression is given by x=−105cos(25°)+125cos(15°)−95cos(61.5°).

The negative sign indicates that the initial leg's displacement (da) is in the opposite direction of the positive x-axis, while the subsequent legs contribute positively. Each term represents the horizontal component of the displacement for the respective leg of the journey.