Rotational energy is usually expressed as a function of ω. Using your Eqn. 2, it should be possible to express as a function of v. Now you can use ratios since the translational energy is known.
Sorry I am somewhat cryptic but I don't want the hall monitors to come down on me.
From Charles Law
V1/T1 = V2/T2
Since V = m/density and Charles Law pertains to a fixed mass you can restate Charles Law in terms of density giving you a relation between density and temperature.
Give this approach a try.
I don't follow what you are doing. The mass you are calculating is based on a density of 1.2 kg/m^3. We know the density has to be lower.
I suggest that you check out Charle's Law. Because it applies to a fixed mass, volume is then inversely related to density. You already have a density at a...
It just occurred to me that the problem or the instructor wants the problem solved by COE. In this case, unless I made a math mistake, I get an answer close to yours. I took the sum of forces approach because it was a more straightforward way of addressing the buoyant force once the diver enters...
What I am trying to say is that the velocity of the diver ( as given in the problem) is somewhat less than what would result from g when falling from the height (as given in the problem). Clearly the diver is accelerating less than g and that is due to the force of air resistance. You can use...
One of the "laws" that led to the ideal gas law will allow a scaling of volume of a given mass of a gas for temperature. That will allow you to use the density given at 12 C without worrying about ideal gas constants or moles.
Don't forget to do calculations in Kelvin!
How does the actual velocity of the diver about to enter the water compare to what would be expected in a vacuum? What would that imply about the actual acceleration?
Assuming your values are for the latter part of the data, a half-life of 81 days shows good agreement with my Chart of the Nuclides (no nerd should be without it) value of 87.2 days for S-35. Remember that this will include a small amount of the shorter lived isotope which will bias the result...
I think you have included all the relevant forces. What answer do you get? Does it agree with the given answer? If not, is the given answer rounded? Are the initial conditions you posted the actual ones given in the problem (transcription errors are common)?
Finally, it never hurts to check...
RPI used to have an Electric Power Engineering Dept. that offered degrees in EP engineering. When I attended in the late 1970's, those guys always had jobs. The program is now part of the ECSE Dept. but I see many of the faculty do EP research.