Answer
(a) v = 15.3 m/s
(b) The average force of air resistance is 1.03 N upwards.
Work Step by Step
(a) Without air resistance, the original potential energy will equal the kinetic energy at the bottom.
$KE = PE$
$\frac{1}{2}mv^2 = mgh$
$v = \sqrt{2gh}$
$v = \sqrt{(2)(9.80 ~m/s^2)(12.0 ~m)}$
$v = 15.3 ~m/s$
(b) The original potential energy plus the work done by air resistance will equal the kinetic energy at the bottom.
$PE + Work = KE$
$Work = KE - PE$
$Fd = \frac{1}{2}mv^2 - mgh$
$F = \frac{\frac{1}{2}mv^2 - mgh}{d}$
$F = \frac{\frac{1}{2}(0.145 ~kg)(8.00 ~m/s)^2 - (0.145 ~kg)(9.80 ~m/s^2)(12.0 ~m)}{12.0 ~m}$
$F = -1.03 ~N$
Note that the force is negative because air resistance did negative work on the ball as it fell. The magnitude of the average force of air resistance is 1.03 N upwards.