Two rock climbers, bill and karen, use safety ropes of similar length. karen's rope is more elastic, called a dynamic rope by climbers. bill has a static rope, not recommended for safety purposes in pro climbing. karen falls freely about 2.0 m and then the rope stops her over a distance of 0.9 m.

The answer is 2.8 times.

Explanation:

Speed needs to be calculated when Karen completes the 2.0m drop, using the following equation:

V^2 = Vo^2 + 2gd = 0^2 + 2*9.81 m/s^2 * 2.0 m = 39.24 m^2/s^2 => V = 6.26 m/s

From there, the rope has a net force which causes a constant acceleration, which can be calculated according to the equation:

Vo = 6.26 m/s

Vf = 0

Vf^2 = Vo^2 + 2ad => a = [Vf^2 - Vo^2]/2d = [0^2 - (6.26 m/s)^2]/2*(0.9m) = -17.63 m/s^2

That acceleration is due to the difference between the force exerted by the rope and Karen's weight:

Karen's weight = mg

Karen's Weight - String Force = Net Force = ma

mg - chord force = ma

String strength = mg - ma = m (g -a) = m [9.81 m/s^2 - (-17.63m/s^2)] = 27.44m

Dividing by weight:

 27.44m/9.81m = 2.79 = 2.8 times

The answer is three times.