Projectile Motion Experiment Calculator

Projectile Motion Lab Analysis

This calculator works in reverse from a classroom projectile experiment. Given launch height, time of flight, and horizontal range, it finds the initial velocity and launch angle that produced the trajectory.

Reverse Projectile Equations

When the projectile lands at ground level after time $t$:

$$V_x = \frac{d}{t}$$ $$V_y = \frac{gt}{2} - \frac{h}{t}$$ $$V = \sqrt{V_x^2 + V_y^2}, \quad \alpha = \arctan\!\left(\frac{V_y}{V_x}\right)$$

Here $h$ is initial height, $d$ is horizontal distance, $t$ is time of flight, and $g = 9.81\,\text{m/s}^2$.

Lab Tips

Measure launch height at the band or release point. Use video timestamps or a stopwatch for flight time. Mark landing spots on tape for accurate range. Repeat trials and average results for better accuracy.

Related tool: Projectile Motion Calculator.

Frequently Asked Questions

What measurements do I need?

You need initial launch height, time of flight, and horizontal travel distance from launch point to landing point.

Why use reverse calculation?

In lab work you measure range and time directly. Working backward finds the launch speed and angle you actually used.

Does air resistance matter?

This model ignores air resistance. Dense projectiles at moderate speeds give the best match to theory.

What if launch height is zero?

Set height to 0. The formula still works and simplifies to standard ground-level projectile motion.

How is maximum height found?

Maximum height equals launch height plus Vy squared divided by twice g, assuming no air drag.

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Projectile Motion Experiment Calculator

Projectile Motion Lab Analysis

Reverse Projectile Equations

Lab Tips

Frequently Asked Questions

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