## Question:

At the instant shown a group of three space-junk fragments with masses ${ m }_{ 1 }$ = 7.45 kg, ${ m }_{ 2 }$ = 3.22 kg, and ${ m }_{ 3 }$ = 8.45 kg are traveling as shown with ${ \upsilon }_{ 1 }$ = 7701m/s, ${ \upsilon }_{ 2 }$ = 6996m/s, and ${ \upsilon }_{ 3 }$ = 6450m/s. Assume that the velocity vectors of the fragments are coplanar, that ${ \overrightarrow { \upsilon } }_{ 1 }$ and ${ \overrightarrow { \upsilon } }_{ 2 }$ are parallel, and that $\theta$ is measured with respect to a line perpendicular to the direction of both ${ \overrightarrow { \upsilon } }_{ 1 }$ and ${ \overrightarrow { \upsilon } }_{ 2 }$. Furthermore, assume that the system is isolated and that, because of gravity, the fragments will  eventually form a single body. Determine the common velocity of the fragments after they come together if $\theta =25°$.