Posted by Brad Paul on September 03, 2002 at 13:03:50:
In Reply to: DE word problem posted by colin on September 03, 2002 at 11:26:42:
: A body with mass m is projected vertically downward with initial velocity v0 in a medium offering resistance proportional to the square root of the magnitude of the velocity. Find the relation between the velocity v and the time t.
: Do I solve for v or t here? How can I tell?
This is an F=ma problem:
1) Pick a positive direction. How about positive is down.
2) Draw a force diagram mg points down and f sqrt(v) points up.
3) Sum the forces and set equal to ma
4) m g - f sqrt(v) = m a
5) Note that a=(dv)/(dt)
6) rewrite :
(dv)/(dt)=g-(f sqrt(v))/m
7) Solve with vo at t=0