Mechanics Problem...HELP!!!

KnifeWRENCH

Hi everyone I'm doing a module in Mechanics at college (and absolutely hating it! ) We were given problems and there's one I can't figure out:

A projectile is launched at an angle A from the edge of a cliff of height H above sea level. If it falls into the sea a distance D from the base of the cliff, prove that the maximum height above sea level is:

H + [(D tanA)^2 / 4(H + D tanA)]

Any help would be greatly appreciated. Thanks.

eZe^

Your final equation has no 'u' in it, therefore you need to eliminate that.


Youll find a value for u^2 when you manipulate the equations Sy= -H and Sx= D...

Max height is Sy, when Vy = 0.

Max height = [u^2 (Sina)^2]/2g

Sub in your value for u^2, youll get Max height equal to,

[(D tanA)^2 / 4(H + D tanA)]

And since it was initially it was a height H above sea level, the actual max height = H + [(D tanA)^2 / 4(H + D tanA)]

JoeB-

It seems to be irrelevant (for this problem) that it was launched from a cliff... the height is simply the max height a projectile will attain when lauched at a certain angle...

On the other hand trying to calculate the distance from the base of the cliff to where it hits the water is more complicated... (isn't it?)

(Trying to remember my applied maths from >12 years ago!)

edit: Actually I just remembered how to solve my second problem, not exceptionally difficult after all but still needs a flash of insight!

The projectile will move horizontally at a constant speed because there's no force acting in that direction, IF we discount air resistance which is often done in these problems)

eZe^

The fact thats its on a cliff is very relevant though. Otherwise the max height would occur at the time its horizontal displacement is D/2... But since itll be moving underneath its initial height you cant make that connection.

JoeB-

Yes, just re-read original post, I got that completely wrong... I thought the height had to be expressed solely in terms of the launch angle 'A' rather than also using the landing distance 'D' from base of cliff... of course the cliff is important in the correctly read question.

I had misread the question, that's why I was saying the thing about the distance 'D' from cliff where it lands... silly me... 'MY BAD' he he.

('My bad' = funny phrase that means nothing.. have heard it used on 'Scrubs' among other things, Scrubs is good)

On a seperate question, Stephen Hawkins says we can't solve the equations of motion for three bodies exactly under Newtons gravity formula... this is obviously correct isn't it? (Because Hawkins says so)
This would have implications for a simulated universe wouldn't it? After all, how would we simulate the motions of the planets if we can't solve the equations exactly? Also, how is it that we say the observed motions are nearly in perfect agreement with Newtons formula if we can't solve the equations exactly? (Do we use 'numerical analysis' or something to get a very close approximation to the correct values?, or do we use high powered computers to 'creep' up on the correct solutions?)
(This is what I was driving at in the 'simulated universe' thread when I said that the universe never gets it 'wrong', I knew in the back of my head that these equations couldn't be solved simultaneausly for all the particles in the universe!)

I may post these questions into the 'simulated universe' thread or start a new thread, I'll see if any answers are put in here first...