Question

mark sits on a swing that is 2.5 feet off the ground. swinging as hard as he can, the swing reaches a height of 6 feet. assuming mark holds a steady pace, the height of the swing could be represented by a cosine curve. if mark makes a full swing forward and backward in 3 seconds, which graph below could represent the height of the swing, in feet, for any time, t?

Explanation:

Step1: Analyze the minimum and maximum heights

The swing starts 2.5 feet off the ground (minimum height) and reaches 6 feet (maximum height). The graph should have values in this range.

Step2: Analyze the period

The period of the swing (time for a full - forward and backward motion) is 3 seconds. The graph should repeat its pattern every 3 seconds.

Step3: Check the given graph

The given graph has values that seem to be in the approximate range of 2.5 - 6 feet and has a pattern that repeats approximately every 3 seconds.

Answer:

The given graph could represent the height of the swing for any time \(t\).