A Fireworks Projectile Explodes High and Away (part 3)

Because air resistance is negligible, $a_{\text{x}}=0$ and the horizontal velocity is constant. The horizontal displacement is horizontal velocity multiplied by time as given by $x=x_0+v_{x}t$, where $x_{\text{0}}$ is equal to zero

where $v_x$ is the x-component of the velocity, which is given by $v_x=v_0\cos {\theta }_0.$ Now,

The time $t$ for both motions is the same, and so $x$ is