What Is the Terminal Velocity of a 70 kg Sky Diver?

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Discussion Overview

The discussion revolves around determining the terminal velocity of a 70 kg sky diver, including the calculation of maximum speed during free fall and the speed after falling 100 meters. The scope includes mathematical reasoning and homework-related problem-solving.

Discussion Character

  • Homework-related, Mathematical reasoning, Technical explanation

Main Points Raised

  • One participant states that the maximum speed of free fall (terminal velocity) is calculated using the equation mg - 0.25V^2 = 0, resulting in Vmax = 52.4 m/s.
  • Another participant suggests finding V(t) by applying Newton's second law again, indicating that the net force acting on the sky diver is mg - k v^2.
  • A third participant notes that the first integration is straightforward, but the second integration to find the position function is complex and suggests using Wolfram Alpha for assistance.
  • A later reply expresses confidence in completing the first integration but acknowledges the difficulty of the second integration.

Areas of Agreement / Disagreement

Participants appear to agree on the approach to finding terminal velocity and the need for integration, but there is no consensus on the methods or solutions for finding V(x) or the position function.

Contextual Notes

The discussion includes unresolved mathematical steps, particularly regarding the integration process needed to find V(t) and subsequently s(t). There are also dependencies on the definitions of forces and parameters involved.

Who May Find This Useful

Students and individuals interested in physics, particularly those studying dynamics and motion under the influence of forces, may find this discussion relevant.

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Homework Statement



A sky diver with a mass of 70 kg jumps from an aircraft. The aerodynamic drag force acting on
the sky diver is known to be FD =kV^2

, where k=.25 N.s^2/m^2

Determine the maximum speed of free fall for the sky diver and the speed reached after 100 m of fall. Plot the speed of the sky
diver as a function of time and as a function of distance fallen


Homework Equations



F=ma

Fg - kV^2 = ma


The Attempt at a Solution



Well I did find Velocity Max to be

mg -.25V^2 = ma

mg - .25V^2 = 0 (a=0 because of terminal velocity)

Vmax = 52.4 m/s

But I am really confused on finding V(x) so I can find the speed at 100m? : /
 
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First find V(t). Apply Newton's 2nd law again:

Fnet = ma = m dv/dt

The forces acting on the sky diver, as you noticed are:

Fnet = mg - k v^2

Now you can solve this differential equation for V(t).

The position function, s(t), can then be found from: V(t) = ds(t) / dt.
 
Great problem. The first integration is pretty straight forward but the second integration to find dx/dt=v is ugly as is the simplifications. I would suggest going to the Wolframalpha.com site for the math.
 
Ok I think I got the first integration but the second ones definitely going to be tricky lol Thanks.
 

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