Can Work-Energy Be Used to Determine Maximum Projectile Height?

[whiskeySierra]

Please forgive me if the answer to this question is obvious, I studied Political Science for three years in undergrad before I realized 'real' science was far more rewarding.

My question (not homework):

I understand that Work-Energy can be used for projectile motion, if what you're after is not time dependent. I also find that working with W.E. is more intuitive for me than the kinematics equations.

Say I have a projectile that is launched at some angle < 90°, at some velocity and I want to know what the maximum height the projectile reaches in its flight. We will assume no air resistance and that height initial = height final.

So figuring out the maximum height of the projectile with kinematics is easy enough, but with W.E. it's not so straight forward.

I know that maximum height along the path would occur where PE has the highest value along the entire path. KE would never be zero because the projectile never stops moving, only slows a little at maximum height.

So how (if possible) can I use W.E. to look at a problem like this?

Thank you.

 

[tiny-tim]

welcome to pf!

hi whiskeySierra! welcome to pf!

I know that maximum height along the path would occur where PE has the highest value along the entire path. KE would never be zero because the projectile never stops moving, only slows a little at maximum height.

So how (if possible) can I use W.E. to look at a problem like this?

ah, but you do know the value of KE at maximum PE …

because you know that the horizontal component of velocity is constant, and that will be the minimum KE (instead of 0)

 

[whiskeySierra]

Could we not say this occurs when the vertical component of velocity is zero?

 

[gneill]

Could we not say this occurs when the vertical component of velocity is zero?

Yes. Energy and momentum conservation laws apply individually and collectively to the vertical and horizontal components of the motion. If you have the initial speed and the launch angle you can immediately determine the initial horizontal and vertical components of the motion including velocity, momentum, and energy. Energy conservation (KE and PE) readily yields the maximum height of the projectile.