Graphs of Projectile Motion Type 3: A bouncing ball

1. Understanding the Motion of a Bouncing Ball

A bouncing ball undergoes vertical projectile motion, meaning it moves under the influence of gravity only, except during the brief moments of contact with the ground.

Key Phases of Motion

1. Upward Motion

• The ball moves upwards after bouncing off the ground.
• It decelerates at −9.8 $m·s⁻²$ (gravity).
• At the highest point, velocity = 0 $m·s⁻¹.$

2. Downward Motion

• The ball accelerates downwards at 9.8 $m·s⁻²$ due to gravity.
• Velocity increases in the downward direction until it reaches the ground.

3. Collision with the Ground

• The ball loses kinetic energy due to an inelastic collision.
• Some energy is lost as heat and sound.
• The ball rebounds with less velocity than before.

4. Repeated Bounces

• Each bounce reaches a lower height due to energy loss.
• The process repeats until the ball comes to rest.

2. Graphs of Motion

Velocity vs Time ($v–t$ graph)

• Alternating positive and negative velocity values.
• Velocity = 0 at each peak.
• Each downward motion is steeper due to acceleration.
• After each bounce, the maximum velocity decreases.

Acceleration vs Time ($a–t$ graph)

• Acceleration remains constant at -9.8 $m·s⁻²$ (gravity).
• Brief positive spike at each bounce due to the ground's force.

Position vs Time ($y–t$ graph)

• Shows parabolic curves for each bounce.
• Each peak is lower than the previous one due to energy loss.

3. Key Takeaways

✔ Gravity always acts downward at -9.8 m·s⁻².

✔ Velocity is zero at the peak of each bounce.

✔ Each bounce reaches a lower height due to energy loss.

✔ Acceleration remains constant except at impact.

Exam Tip

💡 Use consistent sign conventions: Take upward as positive and downward as negative when solving equations.