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March 29, 2024, 08:39:06 pm

Author Topic: 3U Maths Question Thread  (Read 1230616 times)  Share 

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RuiAce

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Re: 3U Maths Question Thread
« Reply #450 on: August 05, 2016, 10:54:48 am »
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massive

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Re: 3U Maths Question Thread
« Reply #451 on: August 05, 2016, 11:08:31 am »
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Thanks Rui!!! Where would I be without you.

Also for the attached equation (SHM) i have to find the speed of the particle when x=2. Do i just sub x=2 into the displacement eqn to get time and then sub that time into the velocity eqn, or is there a better way of doing it? thanks!

RuiAce

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Re: 3U Maths Question Thread
« Reply #452 on: August 05, 2016, 11:37:59 am »
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I'm on my phone so ceebs with LaTeX right now.

If you sub x=2 you will get an infinite number of solutions for t. But then differentiate it to find the velocity and your speed will still be the same.

The more clever way is to differentiate FIRST, then use a Pythagorean identity to write v^2 as a function of x instead. Then sub x=2.

Also, keep in mind speed is the MAGNITUDE of the velocity. The sign should always be positive for speed.
I.e. You want |v|, not v

jamonwindeyer

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3U Maths Question Thread
« Reply #453 on: August 05, 2016, 11:44:00 am »
+2
Thanks Rui!!! Where would I be without you.

Also for the attached equation (SHM) i have to find the speed of the particle when x=2. Do i just sub x=2 into the displacement eqn to get time and then sub that time into the velocity eqn, or is there a better way of doing it? thanks!

That's probably the easiest way in terms of accessibility, but let me show you Rui's way for something different ;D



Now using the Pythagorean identity:



Skipped a few steps, but that should give you the idea!  ;D

-Rui: Popped absolute value brackets around the v. Without the absolute value brackets you need a plus or minus! But thanks for doing the hard stuff Jamon :) -
« Last Edit: August 05, 2016, 11:51:07 am by RuiAce »

Neutron

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Re: 3U Maths Question Thread
« Reply #454 on: August 05, 2016, 12:12:56 pm »
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:O Neutron has something other than a physics question (surprise, i finished my trials :P)

Okay, so for some reason I can't get part ii of this, I feel like I'm just tired and not processing properly, but if one of you kind souls could help that would be great!!

b) A rescue plane is travelling at an altitude of 120 metres above sea level and a constant speed of 216 km/h towards a stranded sailor. A canister containing a life raft is dropped from the plane to the sailor.
i) How long will it take for the canister to hit the water? (Take g=10ms^-2)
A current is causing the sailor to drift at a speed of 3.6 km/h in the same direction as the plane is travelling. The canister is dropped when the horizontal distance from the plane to the sailor is D metres.
ii) What values can D take if canister lands at most 50 metres away from the sailor?

And also, one more! I attached a screenshot :D

Thank you guys!!

RuiAce

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Re: 3U Maths Question Thread
« Reply #455 on: August 05, 2016, 12:32:33 pm »
+1
:O Neutron has something other than a physics question (surprise, i finished my trials :P)

Okay, so for some reason I can't get part ii of this, I feel like I'm just tired and not processing properly, but if one of you kind souls could help that would be great!!

b) A rescue plane is travelling at an altitude of 120 metres above sea level and a constant speed of 216 km/h towards a stranded sailor. A canister containing a life raft is dropped from the plane to the sailor.
i) How long will it take for the canister to hit the water? (Take g=10ms^-2)
A current is causing the sailor to drift at a speed of 3.6 km/h in the same direction as the plane is travelling. The canister is dropped when the horizontal distance from the plane to the sailor is D metres.
ii) What values can D take if canister lands at most 50 metres away from the sailor?

And also, one more! I attached a screenshot :D

Thank you guys!!
I'm in a lecture right now so I'll just address the binomial theorem question.




« Last Edit: August 05, 2016, 12:35:16 pm by RuiAce »

jakesilove

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Re: 3U Maths Question Thread
« Reply #456 on: August 05, 2016, 12:34:45 pm »
+1
:O Neutron has something other than a physics question (surprise, i finished my trials :P)

Okay, so for some reason I can't get part ii of this, I feel like I'm just tired and not processing properly, but if one of you kind souls could help that would be great!!

b) A rescue plane is travelling at an altitude of 120 metres above sea level and a constant speed of 216 km/h towards a stranded sailor. A canister containing a life raft is dropped from the plane to the sailor.
i) How long will it take for the canister to hit the water? (Take g=10ms^-2)
A current is causing the sailor to drift at a speed of 3.6 km/h in the same direction as the plane is travelling. The canister is dropped when the horizontal distance from the plane to the sailor is D metres.
ii) What values can D take if canister lands at most 50 metres away from the sailor?

And also, one more! I attached a screenshot :D

Thank you guys!!

Sorry that it's a bit messy (and handwritten), I just couldn't be bothered typing it up.



You needed to think pretty carefully about what was actually happening, and I think a diagram helped with that. Still, a tricky question, hope my working out makes sense!

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massive

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Re: 3U Maths Question Thread
« Reply #457 on: August 05, 2016, 07:20:11 pm »
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Hey guys how do you determine whether a particle will return to the origin or not??

RuiAce

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Re: 3U Maths Question Thread
« Reply #458 on: August 05, 2016, 07:38:27 pm »
+1
Hey guys how do you determine whether a particle will return to the origin or not??
Does setting x=0 yield a solution?

Or if you analyse it using physics, (as an example) if initially x=0 but then v is monotonic then the particle is of course always going to travel away from the origin.

It depends on the question. The first method is fool-proof but every question is different.

jamonwindeyer

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Re: 3U Maths Question Thread
« Reply #459 on: August 05, 2016, 07:41:45 pm »
+1
Hey guys how do you determine whether a particle will return to the origin or not??

Hey! There are normally two ways:

First, if any expression for position, velocity or acceleration is undefined at the origin, then it will not ever reach there. This doesn't help if it was there once though.

More commonly we just need a bit of intuition. If, for example, velocity and acceleration are both positive for all positive t, then the particle will never return to the origin, it will zoom off to infinity.

Unfortunately, there are no concrete sets of rules for this sort of thing, because there is always some weird exception or counter-argument. It is best to try and practice getting a good look at the whole situation and interpreting your info (we can help with this!)  ;D

massive

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Re: 3U Maths Question Thread
« Reply #460 on: August 05, 2016, 07:47:01 pm »
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what about something like this?

Klexos

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3U Maths Question Thread
« Reply #461 on: August 05, 2016, 10:22:52 pm »
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I have attached my pathetic attempt as well, just for the lols. And my flipped photos are...wow...

Is t formulae question merely just subbing stuff in...?
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RuiAce

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Re: 3U Maths Question Thread
« Reply #462 on: August 05, 2016, 10:27:21 pm »
+1
(Image removed from quote.)
(Image removed from quote.)

I have attached my pathetic attempt as well, just for the lols. And my flipped photos are...wow...

Is t formulae question merely just subbing stuff in...?
Yes it is.

Keep going. You end up with (2+2t)/(2t+2t2) which is just 1/t

Klexos

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Re: 3U Maths Question Thread
« Reply #463 on: August 05, 2016, 10:30:08 pm »
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Yeah I had that result but I don't know what I'm supposed to do with it to make it cot x/2
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Klexos

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3U Maths Question Thread
« Reply #464 on: August 05, 2016, 10:32:12 pm »
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Correct?
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