A space probe of mass M travels through deep space with a constant speed of 10 km/s relative to a nearby observer. At time t=1s, the space probe explodes into 3 unequal pieces. At time t=4s, the largest piece explodes into 3 more pieces, making a total of 5 pieces. The 5 pieces have masses of 0.1M, 0.25M, 0.45M, 0.15M and 0.05M. Relative to the nearby observer, how far did the center of mass of the space ship travel during the 7 second time interval that started at t = Os and ended at t = 7s?

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Chapter1: Units, Trigonometry. And Vectors
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**Scenario: Space Probe Explosion in Deep Space**

A space probe of mass \( M \) travels through deep space with a constant speed of 10 km/s relative to a nearby observer. At time \( t = 1 \) s, the space probe explodes into 3 unequal pieces. At time \( t = 4 \) s, the largest piece explodes into 3 more pieces, making a total of 5 pieces. The 5 pieces have masses of 0.1M, 0.25M, 0.45M, 0.15M, and 0.05M.

**Question:**

Relative to the nearby observer, how far did the center of mass of the spaceship travel during the 7-second time interval that started at \( t = 0 \) s and ended at \( t = 7 \) s?

**Options:**

- \(7 \, [\text{km}]\)

- The question is meaningless since the spaceship explodes partway through the time interval.

- \(70/4 \, [\text{km}]\)

- \(7/M \, [\text{km}]\)

- \(70 \times M \, [\text{km}]\)

- More information is needed regarding the specific details of the five pieces.

- \(70 \, [\text{km}]\)
Transcribed Image Text:**Scenario: Space Probe Explosion in Deep Space** A space probe of mass \( M \) travels through deep space with a constant speed of 10 km/s relative to a nearby observer. At time \( t = 1 \) s, the space probe explodes into 3 unequal pieces. At time \( t = 4 \) s, the largest piece explodes into 3 more pieces, making a total of 5 pieces. The 5 pieces have masses of 0.1M, 0.25M, 0.45M, 0.15M, and 0.05M. **Question:** Relative to the nearby observer, how far did the center of mass of the spaceship travel during the 7-second time interval that started at \( t = 0 \) s and ended at \( t = 7 \) s? **Options:** - \(7 \, [\text{km}]\) - The question is meaningless since the spaceship explodes partway through the time interval. - \(70/4 \, [\text{km}]\) - \(7/M \, [\text{km}]\) - \(70 \times M \, [\text{km}]\) - More information is needed regarding the specific details of the five pieces. - \(70 \, [\text{km}]\)
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