MHB Non-dimensional differential equation 2

AI Thread Summary
The discussion centers on a non-dimensional differential equation for height, specifically h(μ) = (1/μ) - (1/μ²) log_e(1+μ) for small values of μ. Participants express confusion about how to begin solving the problem, particularly in determining the non-dimensional time for a body to fall from the highest point to the ground and its speed upon return. There is a suggestion that crucial information may be missing from the problem statement, which hinders progress. Additionally, it is noted that this problem resembles previous threads initiated by the same user. Clarification on the problem's parameters is necessary for further analysis.
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Consider non-dimensional equation for the height at the highest point is given by
\begin{equation} h(\mu)= \frac{1}{\mu}- \frac{1}{\mu^2} \log_e(1+\mu) \end{equation}
$0<\mu\ll 1.$
Determine to $O(\mu)$, the (non-dimensional) time for the body to travel from the highest point to the ground, and determine an estimate for the (non-dimensional) speed of the body when it returns to the ground, again to $O(\mu)$.

=> I really don't how to start this question. please help me.
 
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grandy said:
Consider non-dimensional equation for the height at the highest point is given by
\begin{equation} h(\mu)= \frac{1}{\mu}- \frac{1}{\mu^2} \log_e(1+\mu) \end{equation}
$0<\mu\ll 1.$
Determine to $O(\mu)$, the (non-dimensional) time for the body to travel from the highest point to the ground, and determine an estimate for the (non-dimensional) speed of the body when it returns to the ground, again to $O(\mu)$.

=> I really don't how to start this question. please help me.

You do not have enough information to say anything about the time.
Is there some information missing from the problem statement?

Btw, this problem looks *a lot* like 2 other threads you started.
Are they perhaps all about the same problem?
 
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