Can Someone please help me with this differential equation

Jun 2019
3
0
Brighton
Accounting for viscous drag and fuel-burning, the one-dimensional equation of motion for a rocket-propelled vehicle travelling along a horizontal surface is

m dv/dt=-1/2 ρAC_D v^2-k dm/dt

where is the density of air, is the effective frontal area of the vehicle, is the drag coefficient, is the rocket’s thrust coefficient. Furthermore, if the mass of the vehicle after fuelling is and the fuel burn rate is a linear , then one may write

m=3000-6t


  • Substitute this expression for and the values of , , and into the differential equation above to show that

dv/dt=(18,000-0.15v^2)/(3000-6t)

How solve this numerically using Euler’s method in Excel with the initial condition and the step size?
 

topsquark

Forum Staff
Jan 2006
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