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 The Trek BBS I need some calculus help.
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August 26 2009, 06:44 AM   #1
MIB

Location: Someplace where I can watch you
I need some calculus help.

After spending a good hour and a half on some homework there is still one lingering question that keeps thwarting my attempts to answer. (Or, more accurately, my answers aren't being accepted by the math study program I'm using.) If anyone can point me in the right direction with this one, I'd greatly appreciate it. The problem reads as follows:

 Use the position function s(t) = –16t^2 + 750, which gives the height (in feet) of an object that has fallen for t seconds from a height of 750 feet. The velocity at time t = a seconds is given by the following. Limit as t -> a (S(a) - S(t)) / (a - t) If a construction worker drops a wrench from a height of 750 feet, how fast will the wrench be falling after 3 seconds?
The hell of it is that the question after this one is very similar and I answered it just fine without resorting to asking for help.
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August 26 2009, 07:25 AM   #2
Iasius

Re: I need some calculus help.

I'm not really sure what I can write here that isn't pretty much the answer already.

Velocity is the first derivative of position is what ...
 The velocity at time t = a seconds is given by the following. Limit as t -> a (S(a) - S(t)) / (a - t)
... is saying.

Point being, I don't really understand your problem with this if you don't explain a bit.
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 August 26 2009, 07:49 AM #3 think Rear Admiral     Location: Cogito ergo sum Re: I need some calculus help. negative (nine times 16) 16X9=acceleration going to say 16X3=velocity just because LOL you need velocity right feet per sec not feet per sec squared ? Don't make me get the physics book for some formula I have intensionally forgotten. __________________ I am a professional human being specializing in managing my emotions because I can barely manage anything else. Would you stop eating those things??? already? Trek sims site @ http://www.starbase118.net
 August 26 2009, 07:53 AM #4 Rocketman Guest Re: I need some calculus help. It may be easier to understand if you try plugging in values for a and t that are both very close to three.
 August 26 2009, 08:06 AM #5 Asbo Zaprudder Rear Admiral     Location: On the beach Re: I need some calculus help. Don't they teach equations such as "v = u + a.t" and the Metric system any more? Anyway, plugging in the values gives s(3) = 606 ft, and so (606 - 750)/(3 - 0) = -48 ft/s is your answer. Just that v = 0 - 16.3 = -48 ft/s seems a lot more direct way of getting to it. Might not stop your Polar Explorer crashing into Mars, 'though.
August 26 2009, 08:14 AM   #6
Iasius

Re: I need some calculus help.

 Great Mambo Chicken wrote: Don't they teach equations such as "v = u + a.t" and the Metric system any more? Anyway, plugging in the values gives s(3) = 606 ft, and so (606 - 750)/(3 - 0) = -48 ft/s is your answer. Just that v = 0 - 16.3 = -48 ft/s seems a lot more direct way of getting to it. Might not stop your Polar Explorer crashing into Mars, 'though.
That's the average speed over the first three seconds, not the velocity after three seconds.

v(t) = ds(t) / dt = -32t

The velocity after three seconds is v(3) = -96.

Don't they teach s(t) = 1/2 * a * t² + v0 * t + h anymore?
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 August 26 2009, 08:37 AM #7 Asbo Zaprudder Rear Admiral     Location: On the beach Re: I need some calculus help. Lol. I won't be sending any probes to Mars.
 August 26 2009, 03:22 PM #8 MIB Rear Admiral   Location: Someplace where I can watch you Re: I need some calculus help. I appreciate the help, guys. However, I was actually able to solve this one afterall. Which, in turn, underlined how important sleep is. I sat and stared at this problem for 30 minutes while I was dead tired (big mistake). Finally, I went to bed and after getting some sleep I was able to solve it with no problem within 30 seconds. Again though, I do appreciate your help. The Mars probes no doubt appreciate it as well. __________________ The sooner we get this relief in the hands of the American people, the sooner they can begin to do their job of being good consumers.--Rep. John Boehner, R-Ohio Government: To them we are not citizens anymore. We're mindless machines.
August 26 2009, 04:01 PM   #9
Solstice
Sexy Wizard

Location: I'm so lost T_T
Re: I need some calculus help.

 MIB wrote: I appreciate the help, guys. However, I was actually able to solve this one afterall. Which, in turn, underlined how important sleep is. I sat and stared at this problem for 30 minutes while I was dead tired (big mistake). Finally, I went to bed and after getting some sleep I was able to solve it with no problem within 30 seconds. Again though, I do appreciate your help. The Mars probes no doubt appreciate it as well.
This is good advice for life in general. If something's stumping you, walk away from it for a while. Get something to eat. Get some rest. Do something fun. Do anything but think directly about the problem. You'd be surprised how often something just pops into your head and you realize you know what to do now.

I have a whole list of "oblique strategies" for this very purpose.
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August 26 2009, 06:55 PM   #10
trekkiedane

Location: I'll let you know when I get there.
Re: I need some calculus help.

 Robert Maxwell wrote: This is good advice for life in general. If something's stumping you, walk away from it for a while. Get something to eat. Get some rest. Do something fun. Do anything but think directly about the problem. You'd be surprised how often something just pops into your head and you realize you know what to do now.
Indeed! I concur wholeheartedly! -very good advice
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August 26 2009, 07:58 PM   #11
SmoothieX

Location: Massachusetts
Re: I need some calculus help.

Iasius wrote:
 Great Mambo Chicken wrote: Don't they teach equations such as "v = u + a.t" and the Metric system any more? Anyway, plugging in the values gives s(3) = 606 ft, and so (606 - 750)/(3 - 0) = -48 ft/s is your answer. Just that v = 0 - 16.3 = -48 ft/s seems a lot more direct way of getting to it. Might not stop your Polar Explorer crashing into Mars, 'though.
That's the average speed over the first three seconds, not the velocity after three seconds.

v(t) = ds(t) / dt = -32t

The velocity after three seconds is v(3) = -96.

Don't they teach s(t) = 1/2 * a * t² + v0 * t + h anymore?
I agree with this solution.

s(t) = 1/2*at^2 + V0*t + h. In other words s(t)=h.

Velocity is the rate at which the position is changing. So, take the derivative with respect to time.

v(t) = ds/dt = at = -32t

Acceleration is the rate at which the velocity is changing. So if you ever have to find that, take the derivative of v(t).

a(t) = d^2s/dt^2 = dv/dt = a = -32 ft/s^2, which is the actual rate of acceleration at the Earth's surface.

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