M2 Projectiles
Maths and statistics discussion, revision, exam and homework help.
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M2 ProjectilesI'm given the equation
.
From this I'm meant to show that the maximum value of
as 
varies is 
and that this is achieved when 
.
I get that the maximum value of
occurse when 
, giving me the quadratic equation 
. Solving this quadratic gives me 
, which kinda looks like what I'm aiming for, but it isn't quite right. Can anyone tell me what I should be doing?
Thanks for any help.
ETA: This isn't the full question - the first part is where the projectiles element is, and all it asks is to derive the first equation given above (which wasn't a problem).Last edited by Julii92; 25-07-2012 at 14:42. -
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Re: M2 ProjectilesFor the first bit, there may be better ways, but you can differentiate the expression w.r.t theta. Then as dx/dtheta = 0 at max, 3 of the terms go away, leaving a nice tan theta = a/x.
Now sub this tan theta back into the original expression to get what you need.
Then for the next bit, sub this value of x back into the tan theta = a/x bit (found earlier) and you're there.
Bric -
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Re: M2 ProjectilesYou can get the tan = a/x by completing the square(Original post by Bric)
For the first bit, there may be better ways, but you can differentiate the expression w.r.t theta. Then as dx/dtheta = 0 at max, 3 of the terms go away, leaving a nice tan theta = a/x.
Now sub this tan theta back into the original expression to get what you need.
Then for the next bit, sub this value of x back into the tan theta = a/x bit (found earlier) and you're there.
Bric -
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Re: M2 ProjectilesThanks, seems I'll have to complete C3 and C4 before tackling questions like this.(Original post by Bric)
For the first bit, there may be better ways, but you can differentiate the expression w.r.t theta. Then as dx/dtheta = 0 at max, 3 of the terms go away, leaving a nice tan theta = a/x.
Now sub this tan theta back into the original expression to get what you need.
Then for the next bit, sub this value of x back into the tan theta = a/x bit (found earlier) and you're there.
Bric -
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Re: M2 ProjectilesOn the spec, it says prior knowledge is C1/C2/C3/M1(Original post by Julii92)
Thanks, seems I'll have to complete C3 and C4 before tackling questions like this.
I tried M2 but gave up after I saw trig identities. -
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Re: M2 ProjectilesI think it says C4 aswell - for OCR in any case.(Original post by Jammy4410)
On the spec, it says prior knowledge is C1/C2/C3/M1
I tried M2 but gave up after I saw trig identities.
