(eight-pound object dropped from a height of 5000 feet, where air resistance is proportional to the velocity.)
write the velocity as a function of time if its velocity after 5 secs is approximately -101 feet per second.
In fact, slugs are horrible creatures, best avoided. Just call the mass - it cancels anyway.
The equation of motion is then:
, where is measured vertically upwards
And you can then divide through by , and replace by to obtain:
After separating the variables, integrating, and using , this gives:
So when (and ):
How you are expected to solve this equation for , I don't know (Newton's method?). In fact, I found (but I cheated and used a spreadsheet!)
So the solution is