Simple conservation of energy problem

AI Thread Summary
To determine the height at which a projectile has a velocity of 0.5v, the conservation of energy principle must be correctly applied. The initial kinetic energy (KE) should equal the final gravitational potential energy (GPE) plus the kinetic energy at height h. The correct setup reveals that the total energy when the projectile leaves the ground must be compared to the energy at height h with a velocity of 0.5v. The solution ultimately shows that the height h is 3v²/8g, correcting the initial misunderstanding of the problem. Attention to detail in interpreting the problem statement is crucial for accurate results.
ehilge
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Homework Statement


All I need to do is figure out at what height h above the ground does a projectile have .5v using only v and g in the answer.


Homework Equations


Conservation of energy: KEi=GPEf
.5mv2=mgh


The Attempt at a Solution


so I went ahead and just plugged in .5v or v and solved for h so...
.5(.5v)2=gh
.5(.25v2)=gh
.125v2=gh
h=v2/8g

however, the correct answer is 3v2/8g

so I guess all I need to know is where the 3 came from. I don't see any algebraic errors and I frankly don't have any other ideas
Any help is greatly appreciated,
Thanks!
 
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Hi ehilge! Welcome to PF! :smile:
ehilge said:
.5(.5v)2=gh

.5(v)2=gh

Too clever by half! :biggrin: :wink:
 
You need to set up the conservation of energy equation properly. What's the total energy when the projectile just leaves the ground? What's the total energy when its speed = 0.5v and its height = h? Set those equal.

ehilge said:

Homework Equations


Conservation of energy: KEi=GPEf
.5mv2=mgh
In general, this is not true. It's only true if all the KE is transformed into PE.
 
ok, so I got the correct answer when I set .5mv2=.5m(.5v)2+mgh. I think I actually just read my own question wrong. I thought I was trying to find the height if the initial velocity is .5v but it looks like I needed to find what the height is when the velocity is .5v but the intitial is still v. Oh well, I geuss I better pay more attention next time. Thanks for you help!
 

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