Question

Derive a general formula for projectile motion with the object launched at an angle

Answer 1

Answer:

  y = x tan θ - (g / 2v₀² cos² θ) x²

Explanation:

An equation is called a general formula that relates the position on the x-axis and the height on the body's axis.

Let's write the position on each axis

X axis. No acceleration

         x = v₀ₓ t

Y Axis.  There is the acceleration of gravity

        y = $v_{oy}$ t - ½ g t²

Let's clear the time in the first equation and substitute in the second

       y = v₀ sin θ  (x / v₀ₓ) - ½ g (x / v₀ₓ)²

       y = v₀ sin θ / v₀ cos θ x - ½ g x² / v₀² cos² θ

       y = x tan θ - (g / 2v₀² cos² θ) x²

This is the trajectory equation in projectile launching