Time problem involving Mass and a Pulley?

[cal04]

Homework Statement

Bob and Cathy,two construction workers on the roof of a 20m highbuilding,are about to raise a keg of nails from the ground by means of a light rope which passes over a light and frictinless pulley.

Bob’s mass= M1=93.1kg
Cathy’s mass=M2=66.1kg
The keg’s mass=M3=47.1kg
The nails mass=M4=64.1kg

As they cast off the rope, both workers slip off the roof and the following unfortunate sequence of events takes place. Hanging together on the rope Bob and Cathy strike the ground just as the keg hits the pulley. Unnerved by his fall, bob let's go of the rope and watched in stunned amazement as Cathy ascends rapidly until she blips her head on the pulley, But gamely hangs on to the rope. However, when the keg hits bib on the head, the bottom breaks, the nails spill out, and the empty keg now begins a rapid ascent as Cathy returns to the ground. As the keg hits the pulley Cathy is a little stunned as she lies on bob and let's go of the rope only to be hit on the head one last time as the kegs makes its final descent. Ignoring the possibility of mid air collisions, which only ass insult to injury, how long did it take this industrial accident to run its course? Assume that all collisions with the ground or pulley serve to start each subsequent motion from rest so that each trip and down begins with zero velocity.
T1=
T2=
T3=
T4=
Total Time=

Homework Equations

I can't find the formulas I need for this problem in order to find all 4 times? Please help I've been looking for formulas on this problem for a minute. Thank you Cal

The Attempt at a Solution

 

[Astronuc]

How about an Atwood's machine?

http://hyperphysics.phy-astr.gsu.edu/hbase/atwd.html

 

[m2003]

As a scientist, it is important to approach problems like this with a systematic and analytical mindset. First, we need to identify the given information and the unknowns in the problem. In this case, the given information includes the masses of the individuals and objects involved, the height of the building, and the assumption that all collisions start from rest. The unknowns are the times it takes for each event to occur.

To solve this problem, we can use the formula for calculating the time it takes for an object to fall a certain distance:

t = √(2h/g)

Where t is the time in seconds, h is the height in meters, and g is the acceleration due to gravity (9.8 m/s^2).

Using this formula, we can calculate the times for each event:

T1: Time for Bob and Cathy to fall 20m to the ground together
t = √(2*20/9.8) = 2.02 seconds

T2: Time for the keg to fall back to the ground after hitting the pulley
t = √(2*20/9.8) = 2.02 seconds

T3: Time for Cathy to ascend to the pulley after letting go of the rope
t = √(2*20/9.8) = 2.02 seconds

T4: Time for the keg to fall back to the ground after hitting Cathy on the head
t = √(2*20/9.8) = 2.02 seconds

Total Time = T1 + T2 + T3 + T4 = 2.02 + 2.02 + 2.02 + 2.02 = 8.08 seconds

Therefore, it takes approximately 8.08 seconds for this industrial accident to run its course. However, it is important to note that this solution assumes ideal conditions and does not take into account any potential air resistance or other factors that may affect the actual time.