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.

     
    Acceleration Due to Gravity Calculator (at different altitudes)
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