3. Several years ago, NASA conducted the Lunar CRater Observation and Sensing Satellite (LCROSS)mission to look for evidence of water deep in craters near the south pole of the Moon(www.nasa.gov/mission_pages/LCROSS/main/index.html). Preliminary analysis of the LCROSS data hasalready demonstrated that there are indeed signifcant quantities of water on the Moon—a useful thingto know if we ever decide to build a permanent base on the Moon. The LCROSS spacecraft waslaunched from Earth aboard at Atlas V rocket on 18 June 2009. It was then sent on its way to the Moonby a Centaur transfer stage rocket. On 9 October 2009, while being observed by the LCROSS spacecraft,the Centaur rocket crashed into a crater at the south pole of the Moon creating a huge plume of Lunardust. Instruments on the LCROSS spacecraft measured the spectroscopic properties of this dust andradioed this data back to Earth for analysis. Then, 4 minutes after the Centaur rocket impacted theMoon, the LCROSS spacecraft itself crashed into the Moon. Both the Centaur and LCROSS were movingat 2.5 km/s relative to the Moon when they impacted. The mass of the Centaur transfer stage at timeof impact was 2366 kg, while the mass of the LCROSS spacecraft was 585 kg. a) By what distance wasthe LCROSS spacecraft following the Centaur? b) Determine the change in the velocity of the Moon dueto the impact of the Centaur and LCROSS spacecraft. c) How much more kinetic energy did the Centaurstage transfer to the Moon than LCROSS transfer to the Moon? (image courtesy of NASA).

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Asked Mar 5, 2020
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3. Several years ago, NASA conducted the Lunar CRater Observation and Sensing Satellite (LCROSS)
mission to look for evidence of water deep in craters near the south pole of the Moon
(www.nasa.gov/mission_pages/LCROSS/main/index.html). Preliminary analysis of the LCROSS data has
already demonstrated that there are indeed signifcant quantities of water on the Moon—a useful thing
to know if we ever decide to build a permanent base on the Moon. The LCROSS spacecraft was
launched from Earth aboard at Atlas V rocket on 18 June 2009. It was then sent on its way to the Moon
by a Centaur transfer stage rocket. On 9 October 2009, while being observed by the LCROSS spacecraft,
the Centaur rocket crashed into a crater at the south pole of the Moon creating a huge plume of Lunar
dust. Instruments on the LCROSS spacecraft measured the spectroscopic properties of this dust and
radioed this data back to Earth for analysis. Then, 4 minutes after the Centaur rocket impacted the
Moon, the LCROSS spacecraft itself crashed into the Moon. Both the Centaur and LCROSS were moving
at 2.5 km/s relative to the Moon when they impacted. The mass of the Centaur transfer stage at time
of impact was 2366 kg, while the mass of the LCROSS spacecraft was 585 kg. a) By what distance was
the LCROSS spacecraft following the Centaur? b) Determine the change in the velocity of the Moon due
to the impact of the Centaur and LCROSS spacecraft. c) How much more kinetic energy did the Centaur
stage transfer to the Moon than LCROSS transfer to the Moon? (image courtesy of NASA).

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Expert Answer

Step 1 Subpart (a)

Let V1 be the velocity of the rocket, V2 is the velocity of the spacecraft, the mass of the moon as m, the velocity of the moon before impact as V and the velocity of the moon after impact as V|.

Suppose the time difference between the impacts is t, then distance s between the rocket and the spacecraft is

Physics homework question answer, step 1, image 1

Therefore, the spacecraft was following the rocket by a distance of 600km.

Step 2 Subpart (b)

Using the conservation of momentum of the system at the time of impact of the rocket and the moon,

Physics homework question answer, step 2, image 1

Substituting the values gives

Physics homework question answer, step 2, image 2

...

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