Graph Analysis: Basketball Height as a Function of Time (Y vs X)

Function Graphs with Periodic Motion

Choose the graph that best describes the following:

The height of a basketball (Y) when a player bounces it as a function of time (X).

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Step-by-step written solution

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1

Understand the problem

Choose the graph that best describes the following:

The height of a basketball (Y) when a player bounces it as a function of time (X).

2

Step-by-step solution

When the player dribbles the ball, it starts from hand height and then moves downwards to touch the floor before bouncing up again. This motion is repeated.

In other words, the ball starts from a height, touches the floor at height 0, and then returns to the player's hand repeatedly.

This means that the graph will have an up and down motion and therefore the graph in answer (b) is correct.

3

Final Answer

Weather101010Height

Key Points to Remember

Essential concepts to master this topic
  • Periodic Motion: Basketball bouncing creates repeating up-and-down wave patterns
  • Zero Points: Height equals zero when ball touches ground between bounces
  • Check Pattern: Graph should show regular peaks and valleys with ground contact ✓

Common Mistakes

Avoid these frequent errors
  • Choosing linear or exponential graphs for bouncing motion
    Don't select straight lines or smooth curves for bouncing = wrong motion pattern! Bouncing creates periodic oscillation, not steady increase/decrease. Always look for repeating wave patterns that touch zero (ground level) regularly.

Practice Quiz

Test your knowledge with interactive questions

Is the function in the graph decreasing? yx

FAQ

Everything you need to know about this question

Why does the basketball graph have to touch zero repeatedly?

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Because the basketball hits the ground between each bounce! When the ball touches the floor, its height is exactly zero, so the graph must cross the x-axis at these points.

Should the bounces get smaller over time?

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In real life, yes! Each bounce loses energy due to friction and air resistance. But for this problem, we focus on the basic pattern - regular up and down motion touching the ground.

Why isn't this a straight line going up?

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A straight line would mean the ball is constantly rising at the same rate. But bouncing involves falling down and rising up repeatedly, creating wave-like motion.

How can I tell the difference between bouncing and other motions?

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Look for these clues:

  • Touches zero regularly (hits ground)
  • Has peaks (maximum height)
  • Repeats the pattern (periodic motion)

What if the player holds the ball instead of bouncing it?

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Then you'd see a horizontal line at constant height! The key word 'bounces' tells us the ball moves up and down repeatedly.

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