1. The flight of a particle projected with an initial velocity of $Um{s}^{-1}$ at an angle $\alpha$ above the horizontal is modelled as a projectile moving under gravity only.

The particle is projected from the point  $({x}_{0},{y}_{0})$ with the upward direction being taken as positive, and with the coordinates being expressed in metres. $g{ms}^{-2}$ is the constant of acceleration due to gravity.

Write down expressions for

(i) the $x$-coordinate of the projectile at time $t$ seconds

(ii) the $y$-coordinate of the projectile at time $t$ seconds.