(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A package of mass 5 kg sits at the equator of an airless asteroid of mass 6.3*10^5 kg and radius 48 m, which is spinning so that a point on the equator is moving with speed 2 m/s. We want to launch the package in such a way that it will never come back, and when it is very far from the asteroid it will be traveling with speed 227 m/s. We have a large and powerful spring whose stiffness is 3.0*10^5 N/m. How much must we compress the spring?

2. Relevant equations

Kf = Ui

(1/2) * m * v^2 = (1/2) * ks * s^2

v = sqrt[ (2 * G * M) / ri ]

3. The attempt at a solution

I've listed out the variables I'll be using in this equation:

m = 5 kg

M = 6.3e5 kg

k = 3e5 N/m

r = 48m

I'll get straight to the point, plugging in the variables was easy up to the point where I had to figure out what v was, where I find the escape speed. I used the equation I stated above ( v = sqrt[ (2 * G * M) / ri ] ) to find out the escape velocity needed to figure out how much compression is needed on the spring, and got 5.403e-6.

However, it seems to be a wrong answer, but I have no idea why, but I have a feeling it has something to do with my velocity (which I got a value of 1.3235e-3 m/s), but again I don't know what else to do with it.

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# Spring compression and escape speed

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