$($a$)$ A man stands a distance $d=0\mathrm{.}525m$ from the left end of a plank as shown in the figure. The plank is supported by three cables. Find the tension in each cable $($in N $).$ Assume the plank is uniform, with length $L=2\mathrm{.}00m$ and mass $31\mathrm{.}0$ kg $,$ and the weight of the man is $715$ N $.($Due to the nature of this problem, do not use rounded intermediate values$-$including answers submitted in WebAssign$-$in your calculations.$)$

$($i$)$

Write Newton's second law for the vertical direction. Be sure to account for all four of the vertical forces. Solve your equation for $T_2.$ You may need your result for $T_1.N$

$|)||=\frac{679\mathrm{.}21}{\text{W}\text{r}\text{i}\text{t}\text{e}\text{N}\text{e}\text{w}\text{t}\text{o}\text{n}\text{'}\text{s}se}$

Write Newton's second law for the horizontal direction. Solve your equation for $T_3.$ You may need your result for $T_1.$ N

$($b$)$ What If$?$ The man now begins to walk to the right. If each of the cables can support a maximum tension of $750$ N $,$ which cable fails first?

cable $1$

cable $2$

cable $3$

At what location does this occur $($measured in m from the left end of the plank$)?$

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m