Proof that a projectile comes to rest in a finite distance

[dk123]

Homework Statement

How do I prove that a projectile in a two-dimensional trajectory motion comes to rest in a finite distance when v>0

Relevant Equations

Projectile Motion Equation

equation of motion :

while

 

[haruspex]

Homework Statement:: How do I prove that a projectile in a one-dimensional trajectory motion comes to rest in a finite distance when v>0
Relevant Equations:: F_net = mg-bv

equation of motion dervinghttps://www.physicsforums.com/attachments/262298

https://www.physicsforums.com/attachments/262295 and https://www.physicsforums.com/attachments/262296 => https://www.physicsforums.com/attachments/262297

The equations you posted look like falling through a medium with linear drag. That is clearly not going to come to rest in consequence of those equations. It will come to rest, one presumes, when it lands.
Please post the exact question as given to you.

 

[dk123]

The equations you posted look like falling through a medium with linear drag. That is clearly not going to come to rest in consequence of those equations. It will come to rest, one presumes, when it lands.
Please post the exact question as given to you.

I fixed the question!

 

[SammyS]

Homework Statement:: How do I prove that a projectile in a two-dimensional trajectory motion comes to rest in a finite distance when v>0
Relevant Equations:: Projectile Motion Equation

equation of motion :
View attachment 262306
while
View attachment 262305
View attachment 262308
View attachment 262309

What have you tried?
Where are you stuck?

According of rules of this forum, you must show an attempt at solving/understanding the problem before we can give any help.

 

[haruspex]

I fixed the question!

Only partly. You have posted some equations and your own paraphrase of the question. This still does not make sense since it is obvious from those equations that it will not come to rest in the y direction.
Please post the complete statement of the question as provided to you.