Problem $1$: The figure below shows a $10$ diametral pitch $\backslash (18\backslash$mathrm$\{$~T$\}20^\{\backslash$circ$\}\backslash )$ straight bevel pinion driving a $30$ T gear, and the location of the bearing centerlines. The transmitted load is $\backslash ($ W$\_\{$i$\}=50\backslash$mathrm$\{$lbf$\}\backslash ).$ Determine $($a$)$ the bearing reactions at $\backslash ($ A $\backslash )$ and $\backslash (\backslash$boldsymbol$\{$B$\}\backslash )$ if $\backslash (\backslash$boldsymbol$\{$A$\}\backslash )$ is to take both radial and thrust loads, $($b$)$ the hp of input shaft $\backslash ($ x $\backslash ),$ and the input and output torques on shafts $\backslash ($ x $\backslash )$ and $\backslash ($ y $\backslash ).$ Shaft a is running at $1800$ rpm $.$