Volleyball Serve Projectile Over the Net
This animation traces a volleyball served at 12 m/s and 30° from a height of 0.9 m, decomposing the launch velocity into horizontal and vertical components. It walks through the kinematics equations step by step, computing the time to reach the net at 6.6 m and the ball's height there (2.73 m), comparing it to the 2.4 m net height to confirm the serve clears it. Useful for physics students learning projectile motion and component analysis.
16:9 · every frame verified for overlaps, spacing and edges before rendering
The prompt that made it
Create a professional educational physics animation explaining this projectile-motion problem step by step. PROBLEM: A volleyball player serves a ball from point A with an initial speed of 12 m/s at an angle of 30° above the horizontal. The ball is released from a height of 0.9 m above the ground. The volleyball net is 6.6 m horizontally from point A, and the top of the net is 2.4 m above the ground. The baseline B is 6 m horizontally beyond the net. Use g = 9.8 m/s². Show the complete problem setup clearly, matching the attached reference image. PHYSICS: Initial velocity: v0 = 12 m/s θ = 30° Resolve the initial velocity into components: vx0 = v0 cos(30°) vx0 = 12 cos(30°) vx0 = 10.39 m/s vy0 = v0 sin(30°) vy0 = 12 sin(30°) vy0 = 6.00 m/s Horizontal acceleration: ax = 0 Vertical acceleration: ay = -9.8 m/s² IMPORTANT: The horizontal velocity remains constant. The vertical velocity changes because of gravity. PART A — WILL THE BALL CLEAR THE NET? Show the volleyball player at point A serving the ball. Animate the ball moving along a parabolic trajectory. The horizontal distance from A to the net is: ΔxC = 6.6 m Use horizontal motion: Δx = vx0 t 6.6 = 10.39 tC tC ≈ 0.635 s Then calculate the vertical displacement from the release point: ΔyC = vy0 tC - 1/2 g tC² ΔyC = 6(0.635) - 1/2(9.8)(0.635)² ΔyC ≈ 1.83 m The ball was released at 0.9 m above the ground. Therefore its height at the net is: yC = 0.9 + 1.83 yC ≈ 2.73 m The top of the net is 2.4 m. Clearly show: Ball height at net = 2.73 m Net height = 2.40 m Therefore: 2.73 m > 2.40 m CONCLUSION: "The ball clears the net." Visually show the ball passing above the top of the net with a clear vertical gap. PART B — DOES THE BALL LAND INSIDE THE BASELINE? After passing the net, continue the animation until the ball reaches the ground. The baseline B is 6 m beyond the net. Therefore the horizontal distance from A to B is: 6.6 + 6 = 12.6 m Find the time when the ball reaches the ground. The initial height is 0.9 m, so: Δy = -0.9 m Use: Δy = vy0 t - 1/2 g t² -0.9 = 6tB - 4.9tB² Solve for the positive time: tB ≈ 1.35 s Then calculate the horizontal distance traveled: ΔxB = vx0 tB ΔxB = 10.39(1.35) ΔxB ≈ 14.0 m The baseline is only 12.6 m from point A. Therefore: 14.0 m > 12.6 m CONCLUSION: "The ball lands outside the baseline." Show the ball crossing the baseline and landing approximately 1.4 m beyond it. VISUALIZATION: Show a clean side-view engineering-style diagram. Include: - Volleyball player at A. - Volleyball. - Net at 6.6 m from A. - Net height = 2.4 m. - Baseline B, 6 m beyond the net. - Ground line. - Coordinate axes x and y. - Initial velocity vector v0 = 12 m/s at 30°. - Horizontal velocity component vx0 = 10.39 m/s. - Vertical velocity component vy0 = 6.00 m/s. - Gravity arrow pointing downward. - Parabolic trajectory. - Time counter. - Horizontal and vertical displacement arrows. - Clear labels for all important distances. Show the equations progressively while the animation runs. At the end, show a final summary: v0 = 12 m/s θ = 30° vx0 = 10.39 m/s vy0 = 6.00 m/s Initial height = 0.9 m Net distance = 6.6 m Net height = 2.4 m Ball height at net ≈ 2.73 m Time to net ≈ 0.635 s Flight time ≈ 1.35 s Total horizontal distance ≈ 14.0 m Distance to baseline = 12.6 m FINAL ANSWERS: (a) YES — the ball clears the net. (b) NO — the ball does not land inside the baseline. It lands about 1.4 m outside the baseline. VISUAL STYLE: Make it a polished university-level engineering mechanics animation. Use clean 2D graphics, smooth motion, readable equations, accurate vectors, clear arrows, and a realistic volleyball court and net. Do not use unnecessary decorative elements. Prioritize physics accuracy and visual clarity.
Make the next one in this series
- Extend the animation to check whether the serve lands inbounds at baseline B, 6 m past the net.
- Show how changing the launch angle to 20° or 40° affects whether the ball clears the net.
- Create a companion animation finding the maximum height and total time of flight for this serve.
