Answer:
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.
