Consider a rectangular foam boat $12$ $cm$ wide by $30.7$ $cm$ long by $4.2$ $cm$ deep. Imagine this boat is loaded with enough cargo so the bottom sits $1.8$ $cm$ below the waterline. Determine the initial acceleration of the boat if the the driving mass is $70$ $g$ and the density of water is $\rho=1000$ $kg/m^3$. $a_i=$ $m/s^2$