[deleted] comments on Rational toy buying

[[deleted]]

Showing my work:

C:\Temp>type meow.cpp
#include <iostream>
#include <ostream>
#include <boost/units/io.hpp>
#include <boost/units/pow.hpp>
#include <boost/units/quantity.hpp>
#include <boost/units/systems/si.hpp>
#include <boost/units/systems/si/prefixes.hpp>
#include <boost/units/systems/si/codata/universal_constants.hpp>
using namespace std;
using namespace boost::units;
using namespace boost::units::si;
using boost::units::si::constants::codata::G;

typedef quantity<boost::units::si::time> quantity_time;

int main() {
    const quantity<mass> external_mass(740 * kilograms / kilo);

    quantity<length> remaining_length(17 * centi * meters);

    const quantity<length> final_length(2 * centi * meters);

    quantity_time elapsed_time;

    quantity<velocity> total_velocity;

    while (remaining_length > final_length) {
        const quantity_time t(1 * second);

        const quantity<acceleration> a(G * external_mass / pow<2>(remaining_length));

        const quantity<length> l = total_velocity * t + 0.5 * a * pow<2>(t);

        elapsed_time += t;
        remaining_length -= l;
        total_velocity += a * t;
    }

    cout << elapsed_time << endl;
    cout << total_velocity << endl;
}

C:\Temp>g++ -Wall -Wextra meow.cpp -o meow.exe && meow
10882 s
6.6012e-005 m s^-1

The final velocity is about 9 inches per hour.

(It would be quite possible to modify this to do a fully “realistic” simulation, with the two pairs of masses and the rotation. That’s more work than I want to do at 1 AM, though.)