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Velocity as a function of time -- Terminal Velocity

  • Thread starter alex steve
  • Start date
I am having trouble finding a staring place. My class requires us to use python to solve the equation.

This problem requires me to use eulers method to solve it. My issues is that i am getting confused as of how to find the v(t). Its been a while since i have had to do advance physics like this. Any help would be appreciated.

The question asks:

When jumping from an airplane, you will most often have a parachute to slow your fall. Here let's consider a very simple example in which the frictional drag force is linearly dependent on the velocity:


dv/dt=a−bv


where a and b are constants. In our case a corresponds to the acceleration due to gravity, and b is a constant from drag. Note that the drag force is negative, indicating it opposes the motion. Use the Euler method to solve for v as a function of time and plot your results. A convenient choice of parameters is a=10and b=1. You should find that v approaches a constant value at long times: this is the terminal velocity. If you open your chute immediately after jumping from the plane, you will have vinitial∼1 m/s, but if you wait a minute or so, you will have vinitial∼50 m/s. Plot both v(t) curves on the same plot with a legend.

I am just getting confused with : if the equations says dv/dt = a=bv , where would i insert t for v(t) if the equation has no t except for the dt in the denominator.
 
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Please don't delete the homework template.
I am just getting confused with : if the equations says dv/dt = a=bv , where would i insert t for v(t) if the equation has no t except for the dt in the denominator.
It is a differential equation, you have to solve it first.
 

gneill

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I am just getting confused with : if the equations says dv/dt = a=bv , where would i insert t for v(t) if the equation has no t except for the dt in the denominator.
First, what do you know about Euler's Method?
 
I do not need to know about Euler's method right now . I just need help on figuring out the v(t) equation which is the first step of this problem. I will have to code The euler's method later on.
 

gneill

Mentor
20,484
2,608
I do not need to know about Euler's method right now . I just need help on figuring out the v(t) equation which is the first step of this problem. I will have to code The euler's method later on.
You won't have a v(t) equation. You'll have a dv/dt equation (which you already have). Then you'll apply Euler's Method to that. So you really should read up on Euler's method first. A web search should turn up many references and examples of its application.
 

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