MOMENTUM:

Problem $3\mathrm{.}3\mathrm{.}11-$ Power wheel

A water jet launched at a speed of $\backslash (50\backslash$mathrm$\{$~m$\}/\backslash$mathrm$\{$s$\}\backslash )$ is used to drive a wheel, reaching a rotational speed of $200$ rpm $.$ If the jet has $60$ mm in diameter, what power is the wheel generating?

You can assume that there are many buckets in the wheel, so that water always found a bucket to hit, and that the diameter of the jet remains constant after impacting the bucket

EXPECTED SOLUTIONS: $\backslash ($ P$=87\backslash$mathrm$\{$~kW$\}\backslash )$