A running track consists of two straight 88.5m segments and two semicircles of radius 39.0m as shown in the figure.
Part A was finding the distance a runner travels in one complete lap. d= 422 m. No problem.
Then part B asks for the displacement in x, y components of a runner that runs half a lap like shown in the figure given. Initially my logic was 2x3.14x39 to find the circumference of the complete circle, which was 245 m. That would be the distance from the origin to point A. (0, 245) From origin to point B would be 88.5 m. (88.5, 0) Total distance traveled from A to B came out to be 211 m. (which covered a straight 88.5 segment and 1 semi circle for visual) I tried final minus initial displacement and got -34. But any of the various x.y coordinates I've put in using this number and others has been wrong. This is how we're supposed to go about doing this problem or am I just completely going about it wrong?
-Thanks, hope this makes sense.
To calculate the displacement in x and y components, you need to consider the vector components of the displacement separately. Let's break it down step by step:
1. Start by finding the total distance traveled, which you correctly calculated as 211 m.
2. For the x-component, consider the horizontal displacement. In this case, the runner moves from point A to point B, and the horizontal distance is 88.5 m. So, the x-component of displacement is +88.5 m.
3. For the y-component, consider the vertical displacement. Initially, the runner is at the origin (0, 0) and moves to point A, which is at a distance of 245 m above the origin. The y-component of displacement is +245 m.
4. To find the final displacement vector, take the sum of the x and y components. The final displacement vector for traveling from A to B is (+88.5 m, +245 m).
Note that the negative sign you obtained (-34) was incorrect. The negative displacement indicates movement in the opposite direction, which is not applicable in this case.
Make sure to double-check your calculations and ensure that you're using the correct values for the x and y coordinates.