# Homework Help: Two Parachute Problems

1. Mar 28, 2010

### cgone

Hi all,
So I have these two parachute problems that have been giving me problems any aid you can provide would be much apreciated!

1. The problem statement, all variables and given/known data
A)A probe is to land on the surface of mars and I am required to find out the diameter of the parachute.
Given constance:
m=40kg
g=3.75m/s2
v0=100m/s
vf= 3m/s
x0=100m
Pair=2/3*1.1774
Cd=1.4
A=pi*D2/4 (where D is the unknown diameter of the parachute)

2. Relevant equations

m$$\frac{dV}{dt}$$=mg-$$\frac{1}{2}$$Pair*Cd*AV2

3. The attempt at a solution

I've seprated the variables and simplified to get:

g-$$\frac{k}{m}$$*V2*dV=dt
where k=$$\frac{1}{2}$$PairCdA
$$\sqrt{}$$
So i decomposed the function for integration:
$$\int$$$$\frac{\frac{1}{\sqrt{g}}}{\sqrt{g-\sqrt{\frac{k}{m}}V}}$$+$$\frac{\frac{1}{\sqrt{g}}}{\sqrt{g+\sqrt{\frac{k}{m}}V}}$$
(ignore the second square root on top of the K/m that comes from G, it's only supposed to be on g)

and so that I've integrated to get the following:

$$\frac{1}{\sqrt{g}*\sqrt{\frac{k}{m}}}(Ln(\sqrt{g}-\sqrt{\frac{k}{m}}V))+Ln(\sqrt{g}-\sqrt{\frac{k}{m}}V))=t+c$$

At this point I understand that I can raise everything to E and cancel the +-$$\sqrt{\frac{k}{m}}V$$ but from here I am unsure (also not 100% on the integration)

Also, I have a similar problem however it's not falling, rather slowing down from a parachute (rocket car slowing down from parachute), where I need to find the distance required to stop the car.

Where I was given m$$\frac{dV}{dt}$$=-$$\frac{1}{2}$$Pair*Cd*AV2

So I integrated as a seperable (don't think this is the right way though) to get
$$\frac{-1}{kV}=t+c$$ (a check or direction for this one is all I need)

Thank you!