$9\mathrm{.}46$ A logging boat is towing a log at $1\mathrm{.}5$ m$/$s against a river current that is $1$ m$/$s$.$ The log is $0\mathrm{.}5$ m in diameter and $2$ m long. $($a$)$ Estimate the power required if the axis of the log is parallel to the flow. $($b$)$ Estimate the power required if the axis of the log is perpendicular to the flow. $($c$)$ Explain any reason$($s$)$ why the actual power required may be different than your estimates.