Object $A$ of mass $1kg$ traveling with a speed of $25\frac{m}{sec}$ to the right collides with an identical object $B$ which was initially at rest. After the collision, object A moves with a velocity of $20\frac{m}{s}$ at an angle of $37$ above the horizontal while object $B$ moves at an angle of $53$ degrees below the horizontal. Determine the speed of object B after collision.

$37$

$($A$)$ vec$(v{)}_{Af}$

$($B$)$ vec$(v{)}_{Bf}^{\text{A}\text{f}\text{t}\text{e}\text{r}}$