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#1 2007-03-20 05:53:51

luca-deltodesco
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Registered: 2006-05-05
Posts: 1,470

projectile problem

ive started Mech 2 as an additional module that i don't actually need, but i want to do anyways, but im having trouble with one of the questions on projectiles.

Basicly, a projectile is fired with initial speed u = √ag  where a is a constant, and g is acceleration due to gravity, at angle θ.
it is fired off of a cliff of height b metres.

the first part is to show that:

i did this ok, and then the next part is this:

Show that the maximum value of x (i.e. the value of x when it hits ground at bottom of cliff) as θ varies is

.

i also did this fine after a bit of thought, however i can't quite get the last part.

Show that this is achieved when

this is where i get stuck, anyone help?

Last edited by luca-deltodesco (2007-03-20 05:58:10)


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#2 2007-03-20 06:06:40

luca-deltodesco
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Registered: 2006-05-05
Posts: 1,470

Re: projectile problem


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#3 2007-03-20 06:16:10

luca-deltodesco
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Registered: 2006-05-05
Posts: 1,470

Re: projectile problem

ah wait, i figured it out, i was trying to solve this by simply plugging the value of x = √a(a+2b) into the equation, but it got very messy.

but i remember, if the discriminant is 0, i.e. x IS √a(a+2b) then the value of ax^2 + bx + c = 0, is -b/2a

i.e.

big_smile


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#4 2007-03-20 09:07:49

Stanley_Marsh
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Registered: 2006-12-13
Posts: 345

Re: projectile problem

what is x anyway?


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#5 2007-03-20 09:31:55

luca-deltodesco
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Registered: 2006-05-05
Posts: 1,470

Re: projectile problem

x and y are just the x and y displacements


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#6 2007-03-20 09:35:24

JaneFairfax
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Registered: 2007-02-23
Posts: 6,868

Re: projectile problem

Last edited by JaneFairfax (2007-03-20 10:06:26)

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#7 2007-03-20 09:48:53

luca-deltodesco
Member
Registered: 2006-05-05
Posts: 1,470

Re: projectile problem

a different way of doing it, but with same results wink


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