# Parachute Problem, Figuring out largest load it can hold

1. Apr 16, 2015

### mathguy2

1. The problem statement, all variables and given/known data

A cargo packed for aerial dropping can withstand an impact speed of 20 mph. A 100 foot diameter circular parachute is used for a particular load. What is the largest load (including the chute itself) that can be accommodated by this chute.

2. Relevant equations

Vt = SQUARE ROOT OF EVERYTHING OVER HERE [(2 x W x 32.2(Gravitational Constant) / .1(Coefficient of drag) x Area x .0805 ft cubed]

32.2; .1; and .0805 are unchanging constants.

3. The attempt at a solution

First I converted 20mph to 29.4 ft per sec, this is the plugin for Terminal velocity, Vt
Then I calculated the area of the circular chute. Since r = 50 and using piR2..... I got 7853.91

Then I started solving the equation with all the plugins

And I got 848.24 lbs for W...

Is this correct? Does this look accurate to everyone? I figured I'd ask because its a new chapter and I'm uncomfortable with the problems.

2. Apr 16, 2015

### PhanthomJay

I don't know where your numbers are coming from. Firstly, if you want to calculate the largest load in pounds (weight), don't multiply W by g, W is already in force units. And then, please show how you arrived at the drag factor and that 0.0805 value, and write out the equation you are using for terminal velocity using letter symbols.

3. Apr 16, 2015

### haruspex

Yes, the answer, as a mass, has effectively been computed in slugs.
I got 845 slugs.

4. Apr 16, 2015

### PhanthomJay

W
with a drag coef of 0.1 for a parachute? Where does that come from , seems off by an order of magnitude

5. Apr 16, 2015

### haruspex

I should have clarified that I was trusting the given numbers.

6. Apr 16, 2015

### PhanthomJay

I
Using a drag factor of 0.1 , I get around 845 pounds for the weight. Using a more realistic drag factor of around 1, it's more like 8450 pounds