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Alta
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Is there an approximation for exp(-k*L) with L large but finite??
An approximation for exponential.
- Thread starter Alta
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- Approximation Exponential
AI Thread Summary
An approximation for exp(-k*L) when L is large but finite is under discussion, with the limit as L approaches infinity suggesting a useful approximation. The conversation highlights that while calculus provides insights, the approximation must consider the entire power series rather than truncating it to the first few terms. It is noted that negative exponents complicate the use of simple approximations, as the full series expansion is necessary for accuracy. The discussion emphasizes that k is assumed to be positive, which influences the behavior of the function. Overall, a comprehensive approach using power series is recommended for better accuracy in approximating the exponential function.
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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