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: Analyze potential energy

Potential energy \(U = mgh\) (where \(m\) is mass, \(g\) is acceleration due to gravity, \(h\) is height). As height \(h\) decreases, potential energy decreases.

Step2: Analyze kinetic energy

Kinetic energy \(K=\frac{1}{2}mv^{2}\) (where \(m\) is mass, \(v\) is velocity). As the swing moves down (height decreases), the speed \(v\) increases (due to conversion of potential energy to kinetic energy), so kinetic energy increases.
When moving from \(W\) to \(Z\), at point \(X\), the swing is moving down - height is decreasing (so potential energy decreasing) and speed is increasing (so kinetic energy increasing). At \(W\) the swing is at rest (initial point, kinetic energy is minimum - zero if we consider start from rest, potential energy is maximum). At \(Y\) the swing is moving up (height increasing - potential energy increasing, speed decreasing - kinetic energy decreasing). At \(Z\) the swing is at the other extreme (kinetic energy is minimum - zero if we consider it comes to rest momentarily, potential energy is maximum at that side).

Answer:

X