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

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i didnt get the equation ... how did you get the above equation ?
 
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but how will i get a numerical value like 0.693 in numerator by splving this . i am not getting what to do , ?
 
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
 
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Failure failure failure

Unable to find out the distance please show
 
We don't do the problems for you. You need to figure them out.
 
I am struggling with this problem for a long time. One question I solved but unable to find Distance
 
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.