How Do You Calculate the Diameter of a Parachute Needed for Safe Landing?

AI Thread Summary
To calculate the diameter of a parachute for safe landing, one must determine the force acting on the parachute using the equation F = dp/dt, where dp represents the change in momentum of the air. Given a weight of 100 kg and an air density of 1.2 kg/m^3, the steady-state velocity needed for safe landing can be derived from these parameters. The diameter of the parachute directly influences the force exerted by the air it displaces, which is critical for achieving a safe descent. Understanding the relationship between parachute area, air density, and velocity is essential for this calculation. Ultimately, focusing on these factors will help determine the required parachute diameter for a safe jump.
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Homework Statement


An ideal parachute accelerates all the air it sweeps as it travels, and the air is accelerated from
0 to the parachute's velocity. Using F = dp/dt calculate the force on an ideal parachute of area A as a function of its velocity and the density of air. Assuming you wouldn't break any limbs if you jumped from 5 feet high without a parachute, this tells you what steady-state velocity you would like your parachute to reach. What diameter a circular parachute you would need? Suppose you weigh 100 kg (including the parachute, a spare, and a video camera to document your jump) and the air density is 1.2 kg/m^3

Homework Equations


The Attempt at a Solution



I'm just a little confused about where to start with this one. Any help?
 
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What is the change in momentum of the air molecules in 1 sec?
 
I'm not sure. I've been working on this one for a while, but I haven't gotten very far at all. Any help?
 
The question is "What diameter a circular parachute you would need?" So focus on the diameter of the parachute. What does that affect?

If you prefer, you could think about it a different way: The question says "Using F = dp/dt calculate the force on an ideal parachute..." So what do you need to know in order to calculate that force?
 
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