Question

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

Answer 1

y = x tan θ - (g / 2v₀² cos² θ) x²

Step-by-step 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