Parabolic Projectile from an Elevation Calculator

Parabolic Projectile from an Elevation Calculator

Enter the initial velocity \(v_0\) (m/s), launch angle \(\theta\) (°), and initial elevation \(h_0\) (m) to calculate:
Time of Flight: \[ T = \frac{v_0\sin\theta + \sqrt{(v_0\sin\theta)^2 + 2g\,h_0}}{g} \]
Horizontal Range: \[ R = v_0\cos\theta\,T \]
Maximum Height (relative to ground): \[ H_{max} = h_0 + \frac{(v_0\sin\theta)^2}{2g} \]

* Enter all values in SI units.

Step 1: Enter Parameters

Example: 30 m/s

Example: 45°

Example: 10 m above ground

Example: 9.81 m/s²

Equations used:
Time of Flight: \( T = \frac{v_0\sin\theta + \sqrt{(v_0\sin\theta)^2 + 2g\,h_0}}{g} \)
Horizontal Range: \( R = v_0\cos\theta\,T \)
Maximum Height: \( H_{max} = h_0 + \frac{(v_0\sin\theta)^2}{2g} \)


Practical Example:
For an initial velocity of 30 m/s, launch angle of 45°, initial elevation of 10 m, and \( g=9.81 \) m/s²:
– Time of Flight ≈ \( \frac{30\sin45° + \sqrt{(30\sin45°)^2 + 2 \times 9.81 \times 10}}{9.81} \) s
– Horizontal Range ≈ \( 30\cos45° \times T \) m
– Maximum Height ≈ \( 10 + \frac{(30\sin45°)^2}{2 \times 9.81} \) m