Projectile Motion: explaining why Vi=Vf

[shocklightnin]

How can i show that vi=vf in projectile motion using variables?

Could i just say that since its a parabola we know that vx isn't going to change, but that vy is because it is affected by gravity. so when it reaches max. height, and vy=0, you know that half of the flight is done, and that the object will follow the opposite path it took to get up there, to go back downwards resulting in the same velocity since gravity and vx is constant.

except i don't know how to show this using variables..

 

[pgardn]

How can i show that vi=vf in projectile motion using variables?

Could i just say that since its a parabola we know that vx isn't going to change, but that vy is because it is affected by gravity. so when it reaches max. height, and vy=0, you know that half of the flight is done, and that the object will follow the opposite path it took to get up there, to go back downwards resulting in the same velocity since gravity and vx is constant.

except i don't know how to show this using variables..

you may have to answer why Vx does not change... any forces?

And you could use one of your kinematic equations to show that in the vertical that Vyo is equal to - Vyf when in free fall and assuming the change in position in the vertical is equal to zero.

 

[tiny-tim]

Welcome to PF!

Hi shocklightnin! Welcome to PF!

How can i show that vi=vf in projectile motion using variables?

(I assume you mean for the initial and final heights being the same?)

One of the standard constant acceleration equations will do it.

 

[mathman44]

You could show that the time needed for the mass to get up to height "h" is the same time it takes for the mass to get from height "h" to the ground. Then using this time calculate Vf, and it will = Vi.