Re: DE word problem

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Posted by colin on September 03, 2002 at 13:30:50:

In Reply to: Re: DE word problem posted by Brad Paul on September 03, 2002 at 13:03:50:

: : 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

Thank you... In the book, they show the solution solved for t, not v. I'm confused about why they solved for t not v. Was there any clue in the initial problem statement?

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Re: DE word problem Subhotosh Khan 13:40:05 09/03/02 (0)

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: : : 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 : Thank you... In the book, they show the solution solved for t, not v. I'm confused about why they solved for t not v. Was there any clue in the initial problem statement?

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