Homework Statement
A concave mirror forms an image on a screen twice as large as an object. Both object and mirror are then moved such that the new image is 3x the size of the object. If the screen is moved 75cm, how far did the object move?
Homework Equations
m = image distance / object...
Homework Statement
Note: I think there is a typo here but I'm not sure. Is there supposed to be a comma between the delta t/2 and y_n on K2 and K3, and delta t and y_n on K4?
Homework Equations
See above.
The Attempt at a Solution
Substituting dy/t = z gives
\frac{dz}{dt} = 3z - 2ty -...
v for centripetal force refers to tangential velocity of the rolling object, so its the velocity of the cork rolling down the ramp, assuming the cork has enough friction against the ramp to not slide.
Homework Statement
Given some ElGamal private key, and an encrypted message, decrypt it.
Homework Equations
Public key (F_q, g, b)
Private key a such that b=g^a
Message m encrypted so that r=g^k, t=mb^k
Decrypt: tr^-a = m
The Attempt at a Solution
My problem is finding r^-a...
Compare it to
\sum \frac{2^n}{3^n}
\frac{2^n}{3^n}\cdot\frac{3^n-1}{2^n}
\frac{3^n}{3^n} - \frac{1}{3^n}
1- \frac{1}{3^n}
With limit n->infinity, this = 1
Homework Statement
Where P_n(x) is the nth legendre polynomial, find f(n) such that
\int_{0}^{1} P_n(x)dx = f(n) {1/2 \choose k} + g(n)
Homework Equations
Legendre generating function:
(1 - 2xh - h^2)^{-1/2} = \sum_{n = 0}^{\infty} P_n(x)h^n
The Attempt at a Solution
I'm not sure if that...
Homework Statement
Given the following key, find two plaintext pairs that encrypt to the same ciphertext.
\begin{pmatrix}
9 & 5 \\
7 & 3 \\
\end{pmatrix} (mod \ 26)
Homework Equations
The Attempt at a Solution
Let the two plaintext pairs be (a, b) and (c, d). Let the...
m(t) = m_{0} - dm*t
Thanks, didn't quite think about that one. Forgot to consider that the amount of mass the asteroid picks up in a set amount of time is dependant on its velocity, and is thus not a constant term.
Homework Statement
A rocket of initial mass m_{0} accelerates from rest in vacuum in the absence of gravity. As it uses up fuel, its mass decreases but its speed increases. For what value of m is its momentum p = mv maximum?
Homework Equations
Tsiolkovsky rocket equation:
v(m) = v_e ln...
Note: this is one of the suggested practice problems for my second-year classical mechanics course.
Homework Statement
A spherical asteroid of mass m_{0} and radius R, initially moving at speed v_{0}, encounters a stationary cloud of dust. As the asteroid moves through the cloud, it collects...
Homework Statement
Two 2.04 µC point charges are located on the x axis. One is at x = 1.02 m, and the other is at x = -1.02 m. Determine the electric field on the y axis at y = 0.470 m.
Homework Equations
E = k*q/r^2
The Attempt at a Solution
First I find the distance from one...
Homework Statement
A mass M is attached to a spring with spring constant K. At the equilibrium point of the spring, the mass has a velocity of V.
M = 8.07 kg
K = 113 N/m
V_o = 0.638 m/s
How far does the mass travel until it stops? How long (in seconds) does it take for the mass to travel from...
Here's how I would do it:
First, make one equation. So f(t) - g(t)
Then find the derivative of that equation for both t<3 and t>3. From there you should be able to find the answer to ( a ). Derivatives describe the behavoir of the original equation. They give the slope of the tangent to the...
Homework Statement
Find the horizontal asymptotes for the following equation:
Homework Equations
f(x) = \sqrt{x^2+4x}-\sqrt{x^2+x}
The Attempt at a Solution
First I factored f(x):
f(x) = \sqrt{x}\sqrt{x+4}-\sqrt{x+1}
Then I conjugated it:
f(x) =...
Homework Statement
Explain why sodium chloride will precipitate from a saturated aqueous solution when sodium nitrate is dissolved in this solution.
Homework Equations
no equations.
The Attempt at a Solution
The saturated NaCl solution cannot dissolve any more sodium, so as NaNo3 dissolves...
When I did this in grade 1, I used a 2L pop bottle (one of these: http://www.caymanshoppers.com/images/diet%20sprite%202L.jpg - image found through google), cut off the bottom, filled it with foam sponges, stuck the egg in the middle and added more foam sponges. We couldn't get the egg to break...
A target is suspended on a platform. A dart launcher is placed at ground level and aimed directly at the target along the line of sight (the distance between dart and target can vary infinitely). Assume a bottomless pit below the target. The dart is launched, and regardless of speed, it will hit...