$(12\frac{1}{2}$ points$)$ The two objects shown in the figure collide perfectly elastically with each other. Object $1$ has a mass of $2$ kg and object $2$ has a mass of $3$ kg $.$ Before the collision, the objects are headed directly towards each other. After the collision object $1$ has a speed of $4\frac{m}{s}$ and is moving and an angle ${}_1$ relative to its original direction of motion, and object $2$ has a speed of $5\frac{m}{s}$ and is now moving at an angle of ${}_2$ relative to its original direction of motion. What is the angle ${}_2($in degrees$)$ if ${}_1=60?$

A$.19\mathrm{.}26$

B$.22\mathrm{.}64$

C$.27\mathrm{.}51$

D$.74\mathrm{.}53$

E$.77\mathrm{.}16$