Assignment:
A golf ball is hit at an angle α with the horizontal and moves under gravity with air resistance κv per unit mass, where v is the velocity and κ>0 is a constant. Show that the equation of the path can be written as
z=x(tan?α+g/κu)+g/κ2 log(1-κx/u),
where u is the initial horizontal component of v. If κ is small enough for κ^2 to be neglected, show that the air resistance reduces the range of the golf ball on the horizontal plane by
(8κu3 tan2 α)/(3g2 ).
Provide complete and step by step solution for the question and show calculations and use formulas.