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A golf ball is hit at an angle a with the horizontal and moves under gravity with air resistance kv per unit mass, where v is the velocity and k>0 is a constant. Show that the equation of the path can be written as

z=x(tan(a)+g/ku)+(g/k^2) log(1-(kx/u)),

where u is the initial horizontal component of v. If k is small enough for k^2 to be neglected, show that the air resistance reduces the range of the golf ball on the horizontal plane by

(8ku^3 (tan^2 (a)))/(3g^2 ).

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