Answer
(a) Final velocity = $35.75ft/sec$
(b)Final elevation = $45ft$
Work Step by Step
(a) $\bigtriangleup KE = -500ft.lbf$
$ F = mg\implies m=\frac{F}{g}$
$ m=\frac{100lb.f}{32.2lb.ft/sec^2} * \frac{32.2lb.ft/sec^2}{1lbf} = 100lb$
$\bigtriangleup KE = (1/2)m(v_2^2-40^2)$
$v_2^2 = \frac {2\bigtriangleup KE}{m}+40^2$
$\frac {2\bigtriangleup KE}{m} = \frac{2*-500*32.2}{100} = -322ft^2/sec^2$
$v_2 = \sqrt{1600-322} = 35.75ft/sec$
(b) $\bigtriangleup PE = 1500ft.lbf$
$\bigtriangleup PE = mg(z_2-z_1)$
$z_2 = \frac{1500*32.2}{100*g}+30$
$z_2 = \frac{1500*32.2}{100*32.2}+30$
$z_2 = 15+30 = 45ft$
