Solving a Physics Problem Involving Hyperbolic Sines

[Xkaliber]

Hi everyone,

I was in the middle of solving a physics problem and came across a math term I am having trouble solving. It is the hyperbolic sine term in this equation:

$$T=\frac{2.0x10^{-8}}{sinh^{2}[\frac{\sqrt{130(2.6x10^{10}-130)}}{1.05x10^{-34}}6x10^{11}]+2.0x10^{-8}}$$

When plugging the sinh term into the calculator, I receive an error due to the massive size of the solution. Is there an equivalent method of taking a hyperbolic sine that can be done by hand since the calulator cannot handle the large exponent?

 

[interested_learner]

You have the high road or the low road.

For the low road, get yourself a copy of the CRC Standard Math Tables. It has tables for Hyperbolic Functions.

For the high road there is Mathematica (my favorite) or MatLab.

For myself, even though I have copies of Mathematica and Matlab (both) at my easy disposal, I still like my book of standard math tables at times.

 

[arildno]

Why bother?

HypSine(Humungous) equals 1/2*e^Humungous.

And 1/Superbig is just about zero.

 

[Xkaliber]

Thanks for the replies. I suppose I will just use Mathematica this evening to obtain some number besides zero since it's a probability. Basically, it is the likelihood of a human launching from the Earth's surface at 4 m/s and reaching Jupiter.

 

[interested_learner]

Tell use what the odds are. OK?

 

[HallsofIvy]

Thanks for the replies. I suppose I will just use Mathematica this evening to obtain some number besides zero since it's a probability. Basically, it is the likelihood of a human launching from the Earth's surface at 4 m/s and reaching Jupiter.

Why would you want an answer "besides zero"? Since 4 m/s is well below escape speed from earth, the "probability" of reaching Jupiter (or any thing except Earth itself) is zero.

 

[Xkaliber]

Well, quantum mechanically the probability is not exacly zero. Through the process known as "tunneling", a particle or object can travel through a potential energy barrier, in this case gravity, with its total energy less than the potential energy. I did actually put zero as my final answer in the end since I included my steps for solving the problem. The final probability ended up being something along the lines of $$e^{10^{44}}$$

 

[arildno]

I think you forgot a minus sign somewhere in your exponent.

 

[Office_Shredder]

Actually, thanks to the many worlds variety of quantum mechanics there are $$e^{10^{5000}}$$ ways of a person launching from Earth at 4 m/s. So $$e^{10^{44}}$$ people actually escape Earth for each person that attempts to launch.

*nod*

 

[HallsofIvy]

Actually, thanks to the many worlds variety of quantum mechanics there are $$e^{10^{5000}}$$ ways of a person launching from Earth at 4 m/s. So $$e^{10^{44}}$$ people actually escape Earth for each person that attempts to launch.

*nod*

Are you sure there shouldn't be a negative sign in the exponent? If not, I jump up and down a few times and Jupiter is overrun with people!

 

[Office_Shredder]

Jupiters are overrun with people. But imagine how many Jupiters there are at that point