Question

when does a roller coaster have the most potential energy?
1
2
4
3

Explanation:

Step1: Recall the formula for gravitational potential energy

The formula for gravitational potential energy is \(U = mgh\), where \(m\) is the mass, \(g\) is the acceleration due to gravity, and \(h\) is the height.

Step2: Analyze the height at each point

Since \(m\) and \(g\) are constant for the roller - coaster (assuming mass \(m\) doesn't change and \(g\) is approximately constant near the Earth's surface), the potential energy \(U\) depends only on \(h\). The higher the roller - coaster is (larger \(h\)), the greater the potential energy. Looking at the graph, point \(5\) (assuming it's the highest point among the options, but since the options are \(1\), \(2\), \(3\), \(4\) and if we assume the intended highest among the given options is mis - labeled and we go by the formula - highest \(h\) gives highest \(U\). If we assume the options are as per the given numbers and there is a mis - numbering in the problem's figure description (maybe a typo where the intended highest is one of the options). If we consider the general principle, the point with the maximum height has maximum potential energy.

Answer:

Assuming the highest point among the options (if we consider the formula \(U = mgh\) and the fact that potential energy is maximum when height \(h\) is maximum). If we assume the intended answer is based on height (and if in the figure the highest of the numbered points \(1\), \(2\), \(3\), \(4\) is point \(1\) (maybe a mis - label in the figure where the actual highest of the four options is \(1\))