- #1
Davio
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Homework Statement
y = A cos (kx-wt)
differentiate twice is -A^2k^2 cos (kx-wt)
Why?
Homework Equations
n/a
The Attempt at a Solution
-w^2 A cos (kx-wt)
Calculus Quick Question: Differentiating Twice for Cosine Function Explanation
- Thread starter Davio
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AI Thread Summary
The discussion centers on differentiating the function y = A cos(kx - wt) twice and the confusion surrounding the result of -A^2k^2 cos(kx - wt). Participants emphasize the importance of the chain rule in differentiation and question the presence of A^2 in the provided answer, suggesting it may not be derived correctly. It is noted that treating A as a constant during differentiation can yield the expected result, but this approach may blur the line between calculus and physics. The conversation also includes light-hearted exchanges and encouragement among participants. Ultimately, the focus remains on clarifying the differentiation process for the cosine function.
y = A cos (kx-wt)
differentiate twice is -A^2k^2 cos (kx-wt)
Why?
n/a
-w^2 A cos (kx-wt)
- #2
Hootenanny
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Apply the chain rule.
- #3
arunbg
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Yes, you should use chain rule, but more importantly,what are you differentiating the function with respect to ? The answer the text gave has a quantity A^2, which I believe can't be obtained by differentiating the eqn, wrt any given variable in the function. Please check if you made an errors in copying the answer.
- #4
Hootenanny
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Good catch arunbg, didn't notice that myselfarunbg said:
- #5
arunbg
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Well, on second thought , you can get the answer if you derive the function with respect to x/A treating A as constant (using good old chain rule), but then that would be calculus, not physics 
Oh, and hoot congrats for goin gold, and keep up the good work.
Oh, and hoot congrats for goin gold, and keep up the good work.
- #6
Hootenanny
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Thanks arunbgarunbg said:
, much appreciated. I've not 'seen' you much on the forums lately, hope everything is good at your end.
Neglect gravity other than that of water; neglect friction.
F1=ρgsh=1000*10*1*(1+4)=50000 N;
F1=ρgsh=1000*10*0.1*4=4000 N;
F3=50000-4000=46000 N?
Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system
$$M(t) = M_{C} + m(t)$$
$$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$
$$P_i = Mv + u \, dm$$
$$P_f = (M + dm)(v + dv)$$
$$\Delta P = M \, dv + (v - u) \, dm$$
$$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$
$$F = u \frac{dm}{dt} = \rho A u^2$$
from conservation of momentum , the cannon recoils with the same force which it applies.
$$\quad \frac{dm}{dt}...
I was thinking using 2 purple mattress samples, and taping them together, I do want other ideas though, the main guidelines are;
Must have a volume LESS than 1600 cubic centimeters, and CAN'T exceed 25 cm in ANY direction.
Must be LESS than 1 kg.
NO parachutes.
NO glue or Tape can touch the egg.
MUST be able to take egg out in less than 1 minute.
Grade A large eggs will be used.
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