Question

alexandra is teaching her little sister how to play volleyball. alexandra hits the ball gently over the net, and then she and her sister hit it back and forth several times. which graph could show the height of the ball above the ground over time?

Explanation:

Step1: Analyze the motion of the volleyball

When a volleyball is hit, it follows a parabolic trajectory (projectile motion) due to gravity. Each time it's hit, it should have a similar pattern: starting from some height (when hit), rising to a peak, then falling, and when it's hit again, the process repeats. Also, the initial height when Alexandra hits the ball (first hit) should be non - zero (since she hits it over the net, not from the ground), and the height of each subsequent hit should be relatively consistent (as they hit it back and forth gently, so the energy and thus the height of each hit should be similar).

Step2: Evaluate each graph

• First graph: The peaks are getting higher, which doesn't make sense as gentle hits should have relatively consistent heights.
• Second graph: The ball starts from height 0, but Alexandra hits the ball (so initial height should be non - zero, as she is hitting it over the net, not from the ground).
• Third graph: The ball starts from a non - zero height (consistent with being hit by Alexandra), and each subsequent hit has a similar parabolic shape with relatively consistent peak heights, which matches the motion of a volleyball hit back and forth gently.
• Fourth graph: The peaks are getting higher, which is inconsistent with gentle, repeated hits.

Answer:

The third graph (the one with the blue curves that start from a non - zero height and have consistent peak heights across multiple parabolic arcs)