ANSWER:
5.82 m/s²
STEP-BY-STEP EXPLANATION:
In order to solve the question we make a free body diagram of the situation, like this:
We make the vertical and horizontal force balances, just like this:
[tex]\begin{gathered} \text{Vertical} \\ \\ N-mg\cdot\cos43\degree=0 \\ \\ N=mg\cdot\cos43\degree \\ \\ \text{Horizontal} \\ \\ mg\cdot\sin43\degree-F=ma \end{gathered}[/tex]With these balances we can calculate the value of the acceleration, like this:
[tex]\begin{gathered} \text{ Given:} \\ \\ F=\mu N\leftarrow F=\mu(mg\cdot\cos43\degree) \\ \\ \text{ We replacing} \\ \\ mg\sin(43)\operatorname{\degree}-\mu(mg\cdot\cos43\degree)=ma \\ \\ g\sin43\degree-\mu g\cdot\cos43\degree=a \\ \\ a=g(\sin43\degree-\mu\cos43\degree) \\ \\ \text{ We substitute each value to determine the acceleration:} \\ \\ a=9.8(0.682-0.12\cdot0.731) \\ \\ a=5.82\text{ m/s}^2 \end{gathered}[/tex]The acceleration of the boat and riders is 5.82 m/s²
