Answer
12 seconds
Work Step by Step
We know the x-component of the rock's force as well as the equation for the y-component of the climber:
Climber y: $F_t - mg = -ma $
Rock: x: $F_t = m_{rock}a$
We plug the value for $F_t$ into the climber equation to find:
$m_{rock}a- mg = -ma \\ mg = m_{rock}a + ma \\ a = \frac{mg}{m+m_{rock}} =\frac{ (73 \times 9.81)}{73+940}=.71 \ m/s^2$
Using this, we find t:
$t = \sqrt{\frac{2x}{a}}=\sqrt{\frac{2\times 51}{.71}}=12s$
