A small rocket$-$propelled vehicle weighs $120$ lb $,$ including $15$ lb of fuel. Fuel is burned at the constant rate of $\backslash (2\mathrm{.}9\backslash$mathrm$\{$lb$\}/\backslash$mathrm$\{$sec$\}\backslash )$ with an exhaust velocity relative to the nozzle of $399\backslash (\backslash$mathrm$\{$ft$\}/\backslash$mathrm$\{$sec$\}\backslash ).$ Upon ignition the vehicle is released from rest on the $\backslash (11^\{\backslash$circ$\}\backslash )$ incline. Drag is $\backslash (0\mathrm{.}15\backslash$mathrm$\{$v$\}^\{2\}\backslash ).$ Plot the position of the rocket vs time, determine the velocity at the end of the burn and how far up the ramp the rocket will travel $($including travel after the fuel runs out. Enter $1$ in the answer box to register your problem assignment.

Hints: $(1)$ once your rocket uses up all its fuel, you will need to stop your ODE$45$; $(2)$ from there you will need to use your final state $($position and velocity, and time$)$ as you initial conditions for a second ODE$45$ with the rocket thrust removed from your Differential Equation.

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