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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°.

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