Question

A ball of mass m is projected vertically upwards at a velocity v◦. The ball experiences an air resistance force (in addition to gravity) of the form FR = −αv^2 where α > 0 is constant and v is the velocity, and reaches a maximum height h before it returns back to the point of projection. (a) Write down the equations of motion of the ball during its upward and and downward journeys and show that the maximum height reached is given by

h = a ln[1 + (vo//vl) ^2]

where vl = sqrt(mg/α) and a = (vl)^2/(2g). (b) Show that the velocity of the ball when it returns back to the point of projection is given by

v^2 r = v^2l [1 − exp(−h/a)].

Answer 1