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Solve a differential equation?

M P, student
Posted 8 years ago

Greetings and respect. Please help me to solve this problem by Wolfram Mathematica. parachutist of mass 70 kg jumps from a plane at an altitude of 32 km above the surface of the Earth. Unfortunately, the parachute fails to open. (In the following parts, neglect horizontal motion and assume that the initial velocity is zero.) (a) Calculate the time of fall (accurate to 1 s) until ground impact, given constant g and a force of air resistance given by

F(v)= - c vIvI

This my opinion to answer this question, but I do not get the right answer from Wolfram Mathematica.

DSolve[{70 y''[t]==9.8 70-0.5y'Abs[y'],y[0]==32000,y'[0]==0},y[t],t]

what is your opinion? Thanks...
POSTED BY: M P
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M P
M P, student
Posted 8 years ago 
NDSolve[{70 y''[t] == -9.8 70 - 0.5 y'[t]*Abs[y'[t]], y[0] == 32000, y'[0] == 0}, y, {t, 0, 900}]

how to solve it in Wolfram alpha?
POSTED BY: M P
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Posted 8 years ago
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M P
M P, student
Posted 8 years ago

Thanks ...

POSTED BY: M P
M P
M P, student
Posted 8 years ago
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POSTED BY: M P
M P
M P, student
Posted 8 years ago

how to solve it Wolfram alpha?
POSTED BY: M P

My opinion is that the parachutist should not have asked his ex-wife to pack his parachute.

As to your equation, your sign convention is mixed up. If you want acceleration to be positive (downward) of 9.8, you can't start at 32000 m. You need to use -9.8. Also, you need y'[t], not y'. I would also use NDSolve to get an answer since its a numerical problem.

Solve the homework problem that way but then think about the terminal velocity of the parachutist (which will prove to be quite terminal for him). See if you can get the same (approximate) answer an easier way using that information.

Regards
POSTED BY: Neil Singer
M P
M P, student
Posted 8 years ago

Thank you very much ... Talking to a professor at MIT, is an honor for me.
POSTED BY: M P
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