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A projectile is fired with an initial speed u and at an angle of elevation ®. The air

resistance is known to be quadratic and the terminal velocity has a magnitude vt. Show

that the equations of motion for the projectile can be cast into the form

y' = f (t; y); t >= 0

Using MATLAB solve the differential equations for an initial speed of 200 ms¡1,

an angle of elevation of 45± and a terminal velocity of 250 ms¡1. Plot the trajectory of

the projectile and, on the same graph, plot the trajectory that the projectile would have

in the absence of air resistance. Use a time range that allows both trajectories to at least

return to their initial height, without going significantly beyond that position.