# Equation of trajectory?

**Classical Mechanics**Level 3

A projectile is thrown with a velocity of \(20\text{m/s}\) making an angle of \({45}^{\circ}\) with the horizontal surface. Then find the equation in \(x\) and \(y\) of the trajectory of the projectile.

The equation is of the form \(ax^2 - bx + by = 0\) where \(a\) and \(b\) are positive co-prime integers, then submit the value of \(a + b\).

**Details and assumptions**:-

- Take \(g\)(acceleration due to gravity) as \(10{\text{m/s}}^2\).
- Neglect any air resistance.