Question

olivia is on a swing at the playground. if the swing is moving from w to z, at which point is her kinetic energy increasing and her potential energy decreasing? (based on a starting point of w)
○ w
○ x
○ y
○ z

Explanation:

Step1: Recall Energy Conversion

Kinetic energy (KE) depends on speed ($KE = \frac{1}{2}mv^2$), potential energy (PE) on height ($PE = mgh$). At highest points (W, Z), speed is 0 (max PE, min KE). Moving down, height decreases (PE decreases), speed increases (KE increases).

Step2: Analyze Motion from W to Z

• At W: Highest point, KE = 0, PE max.
• Moving from W to X (or towards the lowest point, like the middle), height decreases (PE ↓), speed increases (KE ↑). Then from the lowest point to Z, height increases (PE ↑), speed decreases (KE ↓). So between W and the lowest point (path to X/Y direction), KE increases, PE decreases. Among options, X is on the way down from W (towards the center), so at X (or the segment from W to the lowest point), KE increases, PE decreases. Wait, but the points: W is start, X is moving down, Y is moving up towards Z? Wait, no—swing motion: from W (left highest) to X (moving down), then to the lowest point (not labeled), then to Y (moving up), then to Z (right highest). Wait, no, the diagram: W is left, X is left-middle, Y is right-middle, Z is right highest. So from W (highest left) to X: moving down (height decreases), so PE decreases, KE increases (since speed increases as she falls down). Then from X to the lowest point (between X and Y), KE max at lowest, PE min. Then from lowest to Y: moving up, PE increases, KE decreases. Then Y to Z: moving up to highest, PE max, KE 0. So when moving from W to Z, the phase where KE increases and PE decreases is when moving down from W (i.e., from W to the lowest point, which includes X). So among the options, X is the point where she's moving down from W, so KE increasing, PE decreasing.

Answer:

X (Option: X)