Answer
$v_f= 12.91m/s^2 $
Work Step by Step
$h_1= h_i = 6m$
$v_i = 7m/s$
$h_f = 0m$
$P_i + K_i =P_f + K_f $
$mgh_i + \frac{1}{2}mv_i^2 =mgh_f + \frac{1}{2}mv_f^2 $
divide the whole eqn by mass:
$gh_i + \frac{1}{2}v_i^2 =gh_f + \frac{1}{2}v_f^2 $
$gh_i + \frac{1}{2}v_i^2 - gh_f= \frac{1}{2}v_f^2 $
$2(gh_i + \frac{1}{2}v_i^2 - gh_f)= v_f^2 $
$\sqrt {2(gh_i + \frac{1}{2}v_i^2 - gh_f)}= v_f $
$v_f=\sqrt {2(gh_i + \frac{1}{2}v_i^2 - gh_f)} $
$v_f=\sqrt {2(g(h_i -h_f) + \frac{1}{2}v_i^2 )} $
$v_f=\sqrt {2g(h_i -h_f) + v_i^2 )} $
$v_f=\sqrt {2\times 9.8(6 -0) + 7^2 )} $
$v_f= 12.91m/s^2 $
