A particle moves vertically under gravity and a retarding force proportional to the square of the velocity. If is its upward or downward speed and we know that , show that its position at time t is given by

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- Aug 14th 2010, 08:39 AMFGT12another linear motion question
A particle moves vertically under gravity and a retarding force proportional to the square of the velocity. If is its upward or downward speed and we know that , show that its position at time t is given by

- Aug 14th 2010, 09:37 AMAckbeet
What have you done so far?

- Aug 14th 2010, 10:58 AMFGT12
I integrated with respect with time twice

however i feel there is a technique to solce DEs that i dont know, because i cannot see where the ln cos... term would come from - Aug 14th 2010, 01:59 PMAckbeet
Your technique for solving the DE is, alas, entirely wrong. The reason is that the function v occurs in the RHS. You can't just integrate with respect to t, and treat v like a constant, when it varies with t. This equation is separable. Try

- Aug 16th 2010, 02:12 AMFGT12
I integrate the above and get

however from here taking the tangent of both sides does not leave anything readily integrable - Aug 16th 2010, 02:50 AMAckbeetQuote:

however from here taking the tangent of both sides does not leave anything readily integrable

- Aug 16th 2010, 02:55 AMFGT12
thanks

- Aug 16th 2010, 02:56 AMAckbeet
You're welcome. Have a good one!