A high$-$speed centipede in $S^{\text{'}}$ is $10\mathrm{.}0cm$ long measured at rest in $S^{\text{'}}.$ A butcher in $S$ holds two cleavers $($A and B$)9\mathrm{.}00cm$ apart $($measured in S$).$ The centipede runs at such high$-$speed $v$ across a chopping block that the butcher measures the length of the centipede to be $8\mathrm{.}00cm.$

$($a$)$ How fast is the centipede moving across the chopping block?

Hint: How are the proper$-$length and contracted length of the centipede related?

$($b$)$ According to the centipede, how far apart are the cleavers? Let both of the cleavers strike the chopping block when $t=0$ according to the butcher.

Hint: This is the same as the centipede measuring the length of chopping block between the two cleavers.

$($c$)$ What are the space$-$time coordinates of Cleaver A and Cleaver B striking the cutting board in the Sframe and in the $S^{\text{'}}-$frame?

Hint$1$: The two events of significance in this problem are when Cleaver A and Cleaver B strike the cutting board. These happen simultaneously in the Butcher's frame $($S$)$ but they are separate events