Recent content by eshaw

You don't really need another equation based on the question. Solve this one equation for the velocity of the astronaut and figure out what velocity the tank has to be moving so that the velocity of the astronaut is towards the spaceship. Since we have chosen the direction away from the ship to...

No you can't assume that. There is a new set of conditions for b) that only indirectly relate to the initial velocity of the astronaut, tank, and gas in part a). gneill has the right idea...

Your problem is that there should be two unknowns on the right hand of the equation. From part a) we know that the astronaut and the tank are now moving together at a speed 2.413. After the astronaut pushes off of the tank we don't know either the velocity of the tank or the velocity of the...

Where did you get the last equation? It is wrong. This is the right expression. x_{e}=\frac{x_{w}(\frac{v}{v_{w}}-1)}{(1-\frac{v}{v_{e}})} You get it from combining 1) and 2)

I did work out the problem, but I can't really help you unless you show some of your own work, so I just gave some hints about what to do. Try finding T by using (2) to find E_{03}=E_{01}-\frac{\eta_{1}E_{02}}{\eta_{2}} Then plug it into (1) and you should get the result easily. Solving...

That was nasty. Lots of algebra and you'll have to use some long division. Try playing around with the formulas a bit.

F = -\frac{dU}{dr} = \frac{mv^2}{r} From these relations you should be able to calculate this easily. Using the equations for gravitational and centripetal force to find U and K.

Finding the amplitude is a bit harder, since it does depend on the starting conditions. Do you know how to solve differential equations and apply starting conditions? I'm going to assume not. So, x is a function of time for the position of the box, the t isn't the period in that equation, it is...

Since the period in a harmonic oscillator only depends on the mass and the spring constant, as soon as the mass changes the period will change almost instantly and won't depend on what the period was before. So, I guess the answer should be .771 based on your work. The period was .983 and now...

You have to show some work before people will help you in more detail. Here are some starting tips though: split up the velocity into x and y components of the velocity and then use those values to figure out the answer to the two questions Doc Al posed.

Sorry LCKurtz, I didn't read this post carefully enough I guess.smyers33 got the correct answer and you gave him all the correct information. So, I kind of wasted my time posting...

Oh, and LCKurz left out one detail. The center of mass is the sum of all the masses in a system times their positions divided by the total mass. So, the answer would be that integral divided by the total mass. You should also check the answer that you got from taking the integral. Mainly watch...

For the linear density change you just use the definition of what a line is. So, p(x)=kx+p(0) I guess. Then use the give value of p(0) and p(50) to find the slope. After that repeat the integration part of the problem.

Like Dick said nabla squared is called the laplacian. Don't forget that r=sqrt{x^2+y^2+z^2}, This problem is going to be a lot of work.

\nabla(\vec{a}\cdot\vec{r})=\nabla(a_{1}x+a_{2}y+a_{3}z)=a_{1}\vec{i}+a_{2}\vec{j}+a_{3}\vec{k}=\vec{a}