Mechanics

ROBBYM · 2008-04-24 22:16:01

A parachutist of mass m, falling vertically with mass m , speed U at height h above ground, he experiences a resistance equal to

show that the velocity at time t is

so this is what i've done so far

from newtons 2nd i get:

which becomes:
where K is the position vector

taking the dot product i with the z components we get

dividing by m

let

then we get:

the integrating factor is

this becomes:

integrating this gives:

which becomes:
where

so

So i get the general solution

Now its obvious this is not the required solution if anyone can please help me to get the complete solution i will be very gratefull

Dragonshade · 2008-04-25 03:39:15

I got this

SInce I never learn calculus physics and dont know how to solve diff equa, but I think you made an extra neg sign there

the net accel = gravity - resistance

And after you solve the general form of z

you have to put when z=h, dz/dt=U, to get the specific form

Last edited by Dragonshade (2008-04-25 03:40:48)

ROBBYM · 2008-04-28 06:31:01

hey i put the extra negative sign in there because its in the negative Z direction so we have the vector -K

I've tried to find the second part of the equation
however i realized the dz/dt is equal to velocity not speed so i'm still not sure how to get the

Last edited by ROBBYM (2008-04-28 06:33:11)

Dragonshade · 2008-04-28 08:53:44

I dont think the resistant is to the same direction as the gravity. thereforce they must be of different sign regardless of the observer

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