Dimentional Anaylsis: Solving for Revolutions

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NASA's Cassini mission released the Huygens probe, which landed on Titan, with a gentle speed of 31 cm/s and rotated at seven revolutions per minute. A user initially miscalculated the number of revolutions completed when Huygens was 160 yards from the spacecraft, arriving at an incorrect answer. After reevaluating the calculations, they realized they needed to convert the distance to centimeters and correctly apply the rotation rate over the time elapsed. Ultimately, the correct number of revolutions completed was determined to be 55. The discussion highlights the importance of accurate unit conversion and understanding rotational speed in dimensional analysis.
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NASA's Cassini mission to Saturn released a probe on December 25, 2004, that landed on the Saturnian moon Titan on January 14, 2005. The probe, which was named Huygens, was released with a gentle relative speed of 31 cm/s. As Huygens moved away from the main spacecraft , it rotated at a rate of seven revolutions per minute.

How many revolutions had Huygens completed when it was 160 yards from the mother ship?


I know the answer is 55 rev; however, I got a completely different answer. I solved for the answer this way:

160yd*(3ft/yd)*(12in/ft)*(2.54cm/in) = x

I then divided x by 31 cm/s, and multiplied it by 420 rev/s.


Any help or advice would be much appreciated. :smile:
 
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How can something that does only 7 revolutions in 60 seconds do 420 revolutions in 1 second?
 
Muphrid said:
How can something that does only 7 revolutions in 60 seconds do 420 revolutions in 1 second?

You're right. I don't know what I was thinking! I did figure out that I needed to divide 7rpm by 60s and multiply that number by 471.948s, which gave to 55rev. :smile:
 
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