Thankyou - I get it now.

No need to help me - I figured it out.

Thank you.

Great idea - thank you very much for that.

I'm sorry for taking this thread off topic (this is a maple forum). I think I've probably got enough material to complete my report now.

Thank you to everyone who has helped me.

After reading through the part of your article about the threshold velocity and time of chute deployment, i've realised that I won't be able to write about it in my report.

The report i'm doing is meant to be a short piece on the safety of parachuting. As much as I would like to write about the threshold velocity, I don't have the space or time to do it (i'm limited to ten pages unfortunately).

I think i'll just include different graphs to show the effect of varying td.

What i'm meant to do is start with a basic model and then add one improvement.

Is there any way the basic model can be improved (simply)  to decrease the impact velocity to make the landing safe? I thought about using the fact that 'g' varies depending on the altitude but I don't know how much this would effect the impact velocity.

My report is all about safety and the problem I have been having is finding a variable which decreases the impact velocity and that won't take too much explaining in a report - not an easy challenge!

Wow - i've actually been using the first article you mentioned to help me with my project. I never thought i'd cyber-meet the man in person!

Your second article will be very useful to me - thank you.

The project i'm doing is focused more on the safety of parachute jumping and how to minimilize risk.
I wanted to find the minimum time before impact that the parachutist must deploy his parachute.

I'm not sure if working out the jerk will help me in my project unless there's a way of decreasing it?

Any feedback that you can give me will be greatly appreciated.

Thank you to everyone who has helped so far.

Ok - I think there is probably an easier way to go about my problem.

Here is my worksheet:

Download 7999_Graph plotter.mws
View file details

It's a basic model of a parachute jump. td is the time at which the parachute opens. x0, k1 and k2 are fixed constants.

I'm trying to find the velocity of impact in terms of td. The way I did it was probably the long way round and ended up with the equation above. Can someone suggest an easier method?

Sorry that's meant to be:

solve({piecewise(t<td,-.049*t-.245*exp(-.2*t)+4.245, t>=td,-.007*t+.03*exp(1.4*td-1.4*t)-.035*exp(1.2*td-1.4*t)-.042*td+4.215-.21*exp(-.2*td))},{t,td});

Thanks but maple still can't solve it if I use exact rationals and in the form you suggested.

Here is the updated code:

solve({piecewise(t=td,-.007*t+.03*exp(1.4*td-1.4*t)-.035*exp(1.2*td-1.4*t)-.042*td+4.215-.21*exp(-.2*td))},{t,td});

Still maple says 'warning, solutions may have been lost'. I have tried different variations of the above but I still get the same message.

Anyone have any ideas?

I still can't solve this equation:

solve(PIECEWISE([-.4900000000e-1*t-.2450000000*exp(-.2000000000*t)+4.245000000, t < td],[-.7000000000e-2*t+.3000000000e-1*exp(1.400000000*td-1.400000000*t)-.3500000000e-1*exp(1.200000000*td-1.400000000*t)-.4200000000e-1*td+4.215000000-.2100000000*exp(-.2000000000*td), td <= t])=0)

I want to find t in terms of td.

I've found the problem - something in my worksheet was conflicting with the equation. I restarted and now it works.

Thanks for your reply.

Version 11.