Assume that a projectile subject to a linear air resistance drag is fired with an initial...

Assume that a projectile subject to a linear air resistance drag is fired with an initial speed υ0 equal to its terminal speed υt, at an elevation angle θ0.

(a) Find parametric solutions x(t) and z(t) for the trajectory of the projectile in terms of the above parameters. Convert the solution to parametric equations of dimensionless variables X(s), Z(s), and s, where .

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(b) Solve numerically the dimensionless parametric equations obtained above to find the angle θ0 at which the projectile must be fired to achieve maximum range.

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(c) Plot the trajectory of the missile corresponding to its maximum range, along with the trajectory that would occur under these same firing conditions but in the absence of air resistance. Use the above dimensionless parameters as plotting variables.

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(d) Using the mass and dimensions of a baseball given in Example 4.3.2, calculate (i) the terminal velocity of the baseball for linear air drag and (ii) its maximum range when launched at this initial velocity and optimum elevation angle.