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$($a$)$ The velocity of the $0\mathrm{.}500kg$ sphere after the collision is $(-0\mathrm{.}70$hat$(i)+3\mathrm{.}00$hat$(j)-8\mathrm{.}00$hat$(k))\frac{m}{s}.$ Find the final velocity of the $1\mathrm{.}50kg$ sphere.

vec$(v)=$

Identify the kind of collision $($elastic$,$ inelastic, or perfectly inelastic$).$

elastic

inelastic

perfectly inelastic

$($b$)$ Now assume the velocity of the $0\mathrm{.}500kg$ sphere after the collision is $(-0\mathrm{.}250$hat$(i)+0\mathrm{.}775$hat$(j)-1\mathrm{.}70$hat$(k))\frac{m}{s}.$ Find the final velocity of the $1\mathrm{.}50kg$ sphere.

vec$(v)=\frac{m}{s}$

Identify the kind of collision.

elastic

inelastic

perfectly inelastic a are possible, a positive value and a negative value. Report each with their corresponding final velocities.$)$

a $($positive value$)$

$v_{2f}=,$hat$(k)\frac{m}{s}$

$v_{2f}=,$hat$(k)\frac{m}{s}$

a $($negative value$)$

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