Answer
$v = 6.26~m/s$
Work Step by Step
We can find the work that gravity does on the block.
$W_g = mg~d~cos(180^{\circ})$
$W_g = (1.02~kg)(9.80~m/s^2)(2.00~m)~cos(180^{\circ})$
$W_g = -20.0~J$
We can find the work done by tension.
$W_T = T~d$
$W_T = (20~N)(2.00~m)$
$W_T = 40.0~J$
We can use the work energy theorem to find the kinetic energy of the block as it reaches 2.00 m.
$KE_f = KE_0 + W_g+W_T$
$KE_f = 0 - 20.0~J+40.0~J$
$KE_f = 20.0~J$
We can find the speed of the block.
$KE_f = 20.0~J$
$\frac{1}{2}mv^2 = 20.0~J$
$v^2 = \frac{(2)(20.0~J)}{m}$
$v = \sqrt{\frac{(2)(20.0~J)}{m}}$
$v = \sqrt{\frac{(2)(20.0~J)}{1.02~kg}}$
$v = 6.26~m/s$
