explain the theory of projectile motion in relation to the following equations:

Question

explain the theory of projectile motion in relation to the following equations:
(in relation to a launcher experiment for physics 1)

y = y0 + (v0 sin) t - (1/2) g t2

x = (v0 cos ) t

is the angle of the initial velocity above the horizontal
V0 (m/s) is the initial speed of the ball
t (s) is the flight of the ball from the time it is released to the time its hits the floor.
x (m) is the flight range or the horizontal distance from release point to the landing point
y0 is the initial height of the ball
y is the position of the ball when it hits the ground

Explanation / Answer

Horizontal component of velocity remains the same during the entire motion,
so x = v0 cos *t

In vertical direction, initial velocity = v0 sin in the upward direction and accelereration = g in downward direction

So, from the equation s= ut+ 1/2 at^2, we get

y = y0 + (v0 sin) t - (1/2) g t2

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