Range Equation

[meliora27]

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In Kinematics, what's the correct equation to find the range?

If you're dealing with parabolic motion wrt to x-axis displacement would you use Vox*t

or would you use 2Voxt* with t* being voy/g

or would you use Vo^2sin2(theta) / g

I'm confused with all of these different equations

 

[ThirdEye]

I believe you would use range = (Vo^2 sin(2 theta))/g

 

[Bernoull]

If there's no air resistance (virtually always the case), range is simply horizontal velocity * flight time.

Two things to keep in mind.
1. Since there's no air resistance, Vox=Vfx in other words there's no acceleration in x direction so that velocity is constant throughout flight. (here, I'm only talking about freefall motion).

2. Flight time is determined by vertical velocity and NOT horizontal velocity. The equation u use depends on the nature of flight. Is the obj launched from ground and follows a parabolic path or is it launch horizontally from a cliff etc etc.. Flight Time is 2*(Vy/acceleration) for a parabolic flight (ground-->max height-->ground) otherwise, depending on the variables u have, use one of the kinematics equations with a time variable.

I think it's much better to conceptually understand what the variables/terms represent and their inter-relationships than memorizing when to use what kinematic eq..

But again, range = horizontal velocity * flight time.. horizontal velocity is almost always pretty easy to find, Eq for flight time depends on the nature/symmetry of the flight, worst case scenario, use kinematic Eqs..