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Projectile on an Incline (Downward Motion) Calculator

Projectile on an Incline (Downward Motion) Calculator

Projectile on an Incline (Downward Motion) Calculator

Calculate key parameters for a projectile launched downward on an incline (with the projectile moving downward relative to the plane).
The equations used are:
Time of Flight: \[ t = \frac{2\,v_0\,\sin\left(\phi-\theta\right)}{g\,\cos\phi} \]
Range along the Incline: \[ R = \frac{2\,v_0^2\,\cos\theta\,\sin\left(\phi-\theta\right)}{g\,\cos^2\phi} \]

* Enter the initial velocity (m/s), launch angle (°), incline angle (°), and gravitational acceleration (m/s²). Ensure that the launch angle is less than the incline angle.

Step 1: Enter Parameters

Example: 20 m/s

Example: 20° (measured from the horizontal)

Example: 30° (angle of the incline relative to horizontal)

Example: 9.81 m/s²

Formulas:
Time of Flight: \( t = \frac{2\,v_0\,\sin(\phi-\theta)}{g\,\cos\phi} \)
Range along the Incline: \( R = \frac{2\,v_0^2\,\cos\theta\,\sin(\phi-\theta)}{g\,\cos^2\phi} \)


Practical Example:
For an initial speed of 20 m/s, a launch angle of 20°, an incline angle of 30°, and \( g = 9.81 \) m/s²:
– Time of Flight ≈ \( \frac{2 \times 20 \times \sin(30°-20°)}{9.81 \times \cos30°} \approx \frac{40 \times \sin10°}{9.81 \times 0.866} \approx 0.82\, \text{s} \)
– Range along the Incline ≈ \( \frac{2 \times 20^2 \times \cos20° \times \sin10°}{9.81 \times \cos^2 30°} \approx 7.3\, \text{m} \)

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