Using Newton's 2nd to find optimal launch angle

[Boatman(J)]

Hello. In one of my engineering classes we are doing a computer programming project that requires us to use Newton's second law to find an equation that that would give us the max distance traveled by an object launched off a cliff at a known height of H and an initial velocity of V_o. Then with that equation we would use MATLAB's fzero function to determine the optimal angle from that equation, which would then allow us to find the max distance traveled at the angle.
The equation I found was:

x=(V_o)((sqrt((V_osin(Θ))^2-2g(-H))-V_osin(Θ))/g
​

This was found through kinematics opposed to Newton's Second Law, so I wanted to know how I would go out deriving the equation above (if it were right) through Newton's Second Law of motion?

 

[Khashishi]

kinematics is Newton's laws, so I don't see the problem here. The second law by itself isn't enough; you need the first and third law, too, and then you have kinematics.

 

[A.T.]

This was found through kinematics opposed to Newton's Second Law, so I wanted to know how I would go out deriving the equation above (if it were right) through Newton's Second Law of motion?

It looks like gravity is the only force considered there. And gravity simply accelerates everything by g, which ends up in your equation. You can express it as force of gravity mg accelerating a mass m, but then the m's cancel out and you are left with g again.

In a less trivial example that considers the aerodynamic drag, you will need Newtons 2nd, because you have to combine different forces to net force to get the acceleration.