So I solved this complicated DE and got this equation and trying to solve for Vo(intial velocity). The instructions told us to use Newton's Method or a graphing program to solve for Vo(Matlab,Mathematica, Maple,etc.) Is there any other method to solve?
Vo(-333.3)e^[-0.003*ln(98/0.03Vo)(-333.3)]-3266.67 ln(98/0.03V (-333.3)=10
I have no idea where to start!
Vo(-333.3)e^[-0.003*ln(98/0.03Vo)(-333.3)]-3266.67 ln(98/0.03Vo) (-333.3)=10
Sorry! this was a very complicated one....yeah it started as a first order DE and was simplified in order to find Vo(initial velocity) We were told that it would be virtually impossible to solve this equation without using Newton's method or a graphing program...just wondered was there another way
Assuming that [imath]333.3=\frac{1000}{3}[/imath], and [imath]3266.67=\frac{9800}{3}[/imath], it can be shown that the equation can be rewritten as:
This equation can not be solved for [imath]V_0[/imath], however applying Newton-Raphson on the formula:
gives (x used instead of V0) as recursive equation:
Start with [imath]x_0=0.1[/imath] and you will see that the solution is extremely fast found.
Hope this helps,
Coomast