Answer
(a) Karen will feel a force from the rope which is 3.0 times her body weight.
(b) Jim will feel a force from the rope which is 7.7 times his body weight. Jim is more likely to get hurt.
Work Step by Step
(a) We can use kinematics to find Karen's speed after she falls 2.0 meters.
$v = \sqrt{2ay} = \sqrt{(2)(9.80 ~m/s^2)(2.0 ~m)} = 6.26 ~m/s$
We can use this velocity as $v_0$ to find the rate of deceleration at which Karen comes to a stop.
$a = \frac{v^2-v_0^2}{2y} = \frac{0 - (6.26 ~m/s^2)^2}{(2)(1.0 ~m)} = 19.6~m/s^2 = 2.0g$
$\sum F = ma$
$F_T - mg = 2.0mg$
$F_T = 3.0mg$
Karen will feel a force from the rope which is 3.0 times her body weight.
(b) We can use the same velocity $v_0 = 6.26 ~m/s$ to find the rate of deceleration at which Jim comes to a stop.
$a = \frac{v^2-v_0^2}{2y} = \frac{0 - (6.26 ~m/s^2)^2}{(2)(0.3 ~m)} = 65.3~m/s^2 = 6.7g$
$\sum F = ma$
$F_T - mg = 6.7mg$
$F_T = 7.7mg$
Jim will feel a force from the rope which is 7.7 times his body weight.
Jim is more likely to get hurt.
