What do you mean by projectile motion and projectile particle? Find the value of the position of a projectile particle at any instant of time.

(N/A) Projectile Motion: When an object is thrown into the Earth's gravitational field,it moves with a constant horizontal velocity and a constant vertical acceleration. Such a two-dimensional motion is called projectile motion,and the object is called a projectile.
For example,when we kick a football,it performs projectile motion if air resistance is neglected.
$A$ projectile has motion along a horizontal path with uniform velocity $(a_x = 0)$.
$A$ projectile has motion along a vertical path under gravity with uniform acceleration equal to $g$ $(a_y = -g)$.
Suppose the projectile is launched with velocity $\vec{v}_0$ at an angle $\theta_0$ with the $X$-axis. The acceleration is $\vec{a} = -g \hat{j}$.
The initial velocity components are:
$v_{0x} = v_0 \cos \theta_0$
$v_{0y} = v_0 \sin \theta_0$
Using the kinematic equation $r = r_0 + v_0 t + \frac{1}{2} a t^2$:
For the $X$-coordinate:
$x(t) = x_0 + v_{0x} t + \frac{1}{2} a_x t^2 = 0 + (v_0 \cos \theta_0) t + 0 = v_0 \cos \theta_0 t$
For the $Y$-coordinate:
$y(t) = y_0 + v_{0y} t + \frac{1}{2} a_y t^2 = 0 + (v_0 \sin \theta_0) t - \frac{1}{2} g t^2 = v_0 \sin \theta_0 t - \frac{1}{2} g t^2$
Thus,the position of the particle at any instant $t$ is given by the coordinates $(x(t), y(t)) = (v_0 \cos \theta_0 t, v_0 \sin \theta_0 t - \frac{1}{2} g t^2)$.