Projectile on an Incline Calculator

Projectile on an Incline Calculator

Calculate the parameters of a projectile launched from the base of an inclined plane.
The projectile is launched with an initial velocity \( v_0 \) at an angle \( \theta \) relative to the horizontal, while the plane is inclined at an angle \( \beta \).
Ensure that \( \sin\theta > \cos\theta\,\tan\beta \) so that the projectile moves upward along the incline.

* Enter the initial velocity, launch angle, incline angle, and gravitational acceleration.

Step 1: Enter Parameters

Example: 20 m/s

Angle relative to horizontal

Angle of the incline relative to horizontal

Default: 9.81 m/s²

Derived Formulas:
Time of Flight: \( T = \frac{2v_0\Bigl(\sin\theta-\cos\theta\,\tan\beta\Bigr)}{g} \)
Range along the Incline: \( R = \frac{2v_0^2\,\cos\theta\,\sin(\theta-\beta)}{g\,\cos^2\beta} \)
Maximum Height above the Incline: \( H_{\text{inc}} = \frac{v_0^2\,\sin^2(\theta-\beta)}{2g\,\cos^2\beta} \)


Example:
For \( v_0 = 20\,\text{m/s} \), \( \theta = 50^\circ \), \( \beta = 30^\circ \), and \( g = 9.81\,\text{m/s}^2 \), the calculator computes the time of flight, range along the incline, and maximum height above the incline.