Answer
(a) $a = 0.832~m/s^2$
(b) $t = 17.3~s$
Work Step by Step
(a) Let's consider the top point on the chain which will have the most tension. Let's assume that the tension at the top of the chain is 2.5 times the weight of the chain. We can find the acceleration for this situation.
$\sum F = ma$
$T - mg = ma$
$a = \frac{T-mg}{m}$
$a = \frac{(2.5\times (575~kg)(9.80~m/s^2))- (575~kg+750.0~kg)(9.80~m/s^2)}{575~kg+750.0~kg}$
$a = 0.832~m/s^2$
(b) We can find the time it takes to get the boulder out of the quarry.
$y = \frac{1}{2}at^2$
$t = \sqrt{\frac{2y}{a}} = \sqrt{\frac{(2)(125~m)}{0.832~m/s^2}}$
$t = 17.3~s$
