A $0\mathrm{.}500kg$ sphere moving with a velocity given by $(2\mathrm{.}00$hat$(i)-2\mathrm{.}50$hat$(j)+1\mathrm{.}00$hat$(k))\frac{m}{s}$ strikes another sphere of mass $1\mathrm{.}50kg$ moving with an initial velocity of $(-1\mathrm{.}00$hat$(i)+2\mathrm{.}00$hat$(j)-3\mathrm{.}30$hat$(k))\frac{m}{s}.$

$($a$)$ The velocity of the $0\mathrm{.}500kg$ sphere after the collision is $(-1\mathrm{.}00$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$(v)=,\frac{m}{s}$

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$(i)+0\mathrm{.}875$hat$(j)-2\mathrm{.}23$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

positive value and a negative value. Report each with their corresponding final velocities.$)$

a $($positive value$)$

$v_{2f}=$

hat$(k)\frac{m}{s}$

$a($negative value$)$

$v_{2f}=$

hat$(k)\frac{m}{s}$