Chapter 8 - Potential Energy and Conservation of Energy - Problems - Page 207: 59a

$h =19.44m/s$

Subscript: i = initial f= final a = air resistance $ mass = \frac{weight}{gravity}$ $mass = \frac{5.29}{9.8}$ $mass = 0.54$ $K_i = E_a +U_f $ $\frac{1}{2}mv^2 =F_ah +mgh$ $\frac{1}{2}\times 0.54\times 20^2 = (0.265\times h) +(5.29\times h)$ $108 = h(0.265+5.29)$ $108 = h(5.555)$ $h = \frac{108}{5.555}$ $h =19.44m/s$