How Do You Derive the Distance Traveled by a Projectile in a Viscous Liquid?

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The discussion focuses on deriving the distance traveled by a projectile in a viscous liquid, where the retarding force is proportional to the square of the velocity. The user successfully solved for the time required to reduce the velocity to half but struggles with deriving the distance. Key points include the need to apply the correct differential equation and the method of separation of variables. The conversation emphasizes the importance of integrating the velocity to find the distance, with hints provided on how to approach the problem. Overall, the user expresses frustration and urgency as an exam approaches, highlighting the challenge of understanding the mathematical concepts involved.
  • #31
i didnt get the equation ... how did you get the above equation ?
 
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  • #32
ok got it
 
  • #33
but how will i get a numerical value like 0.693 in numerator by splving this . i am not getting what to do , ?
 
  • #34
but how will i get a numerical value like 0.693 in numerator by solving this by integration to obtain S .

i am not getting what to do , ? Totally puzzed , please do the rest please
 
  • #35
Start by using the velocity equation to find the time at which the velocity is half its initial value.

Chet
 
  • #36
IMG_20151009_181318.jpg
 
  • #38
Failure failure failure

Unable to find out the distance please show
 
  • #39
Log and all coming
 
  • #40
Please show
 
  • #41
We don't do the problems for you. You need to figure them out.
 
  • #42
Give some hint then
 
  • #43
I am struggling with this problem for a long time. One question I solved but unable to find Distance
 
  • #44
Supposedly you got the velocity, and then all you've written about getting the position is "failure failure failure."

Here's a hint: Try again.

The relationship between acceleration and velocity is analogous to that between velocity and position. If you understood how to get v from a, it's exactly the same mathematical process to get x from v.
 
  • #45
romiomustdie said:
Please show
dx=Vdt
 

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