(Solved): Gear \( A \) on the drive shaft of the outboard motor has a radius \( r_{A}=8 \) in. and the meshe ...

Gear \( A \) on the drive shaft of the outboard motor has a radius \( r_{A}=8 \) in. and the meshed pinion gear \( B \) on the propeller shaft has a radius \( r_{B}=40 \) in. The point \( P \) is located on the propeller's tip at a distance 9 in. from the neutral axis of the propeller's shaft. At the beginning of the propulsion, the drive shaft rotates with an angular acceleration \( \alpha=\mathcal{A} . t^{2.4} \) rad.s \( { }^{-2} \) where \( t \) is in seconds. what must be the value of \( \mathcal{A} \) to have, while starting from rest, \( \mathrm{v}_{\mathrm{P}}=22 \) in. \( \mathrm{s}^{-1} \) in 9 seconds?