Physics Projectile Motion Deriviations?

Question

Hey. Can you help me derive these formulas using:
delta V = A (delta T)
delta X = (Initial Velocity) (Time) + (0.5) (-9.81) (time squared)

The formulas are:

(Total distance in y) = (abs value of V)^2 (sin (angle of release))^2 / (-9.81)

Height = (0.5) (abs value of V) (sin (angle of release))^2 / (-9.81)


THANKS FOR THE HELP!

Answer 1

The ref. does a far better job than I would.
Your equations are not correct.
I'll use "V" to denote the magnitude of the velocity.
(Total distance in x) = V^2 * sin (2*angle of release) / g
Height = 0.5 Vx^2 / g = 0.5 (V*sin(angle of release))^2/g, in other words not V*sin^2 but (V*sin)^2

Answer 2

If the piece separates gently (and not with an explosion as in case of a fire cracker rocket ) then it will fly side by side as no external force has acted on the stone or the piece. So the correct answer is option 1. In case of an explosion midway it will depend on the point of separation. The small piece can go in any random direction (not necessarily horizontal) and follow different parabolic path.