i've noticed there are three formulas for displacement in projectile motion: dx=vixt, dx=vixt+0.5gt^2 and vfx^2=vix^2+2ad (same for in the y direction). im just confused as to when you use these three, can anyone please clear that up for me?

thanks!

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hotvette
Homework Helper
Is there a specific problem you are trying to solve? You might want to check the equations again. You listed 2 different equations for dx.

hotvette said:
Is there a specific problem you are trying to solve? You might want to check the equations again. You listed 2 different equations for dx.
these equasions relate to projectile motion, and i dont know which one of them to use for what kind of problem: yf=yi problems where they are kicked on level ground or those shot from a cliff. which one of these equasions do use when? and for what type of problems?

OK, you know how you use kinematic equations normally? what you've written are various forms of the kinematic equations, all in the x direction. when you're doing projectile motion, you have axes, x and y. y is commonly vertical, x horizontal. when we fire a projectile, the only thing in common between the x and y planes are time. So, we do each separately.

Depending on what the conditions are, you use different equations. usually for a projectile, there is no acceleration in the x direction. so we use $$\delta x= v_{0x}t$$. when there's acceleration, we have to account for it. usually this is only in the y direction, because in the y direction there is acceleration due to gravity, g. so we use $$\delta y= y_{0} + v_{0y}t + \frac {1}{2} at^2$$ usually we use these in projectile motion problems. You can also use the last equation when you don't know time and you have a change in the velocities.

So, you have to understand what the equations mean and what you're given, and then you use what ever is most appropriate.

HallsofIvy
Homework Helper
The first, dx=vixt, is for constant velocity in the x-direction.

The second, dx=vixt+0.5gt^2, is for constant acceleration, g.
Be careful about applying this "also" to the y direction. Typically g is the acceleration due to gravity and it acts only in one direction!

The third, vfx^2=vix^2+2ad, is really a statement of "conservation of energy" since you can write it as 2ad= vfx^2- vix^2. If you multiply both sides by mass "m", you would have 2amd= vfx^2- vix^2 or ma d= (1/2)mvfx^2- (1/2)mvix^2. The left side is the work done by force= ma acting over distance d and the right hand side is the change in kinetic energy (assuming that vfx and vix are the final and initial velocities, respectively).

This does is NOT a vector equation- there is no "y" version. You must assume that vfx and vix are the speeds in whatever direction the object is moving.