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During July 1994 the comet Shoemaker-Levy 9 smashed into Jupiter in a spectacular fashion. The comet actually consisted of 21 distinct pieces, the largest of which had a mass of approximately 4.0 · 1012 kg and a speed of 6.0 · 104 m/s. Jupiter has a mass of 1.9 · 1027 kg and an orbital speed of 1.3 · 104 m/s. If this piece of the comet had hit Jupiter head on, what would have been the change (magnitude only) in Jupiter’s orbital speed (not its final speed)?

Respuesta :

Answer:

[tex]\Delta V = 6.3*10^{-11} m/[/tex]s

Explanation:

Using conservation of momentum to calculate the final speed, u

MV - mv = (M+m)u

[tex]u = \frac{MV - mv}{(M+m)}[/tex]

The change in speed

[tex]V - u =  V -\frac{MV - mv}{(M+m)}[/tex]

[tex]\Delta V = \frac{MV+mv - MV +mv}{M+m}[/tex]

[tex]\Delta V = \frac{2m}{M+m} v[/tex]

m = mass of comet fragment  = 4.0*10^12 KG

M = mass of Jupiter  = 1.9*10^27 KG

v = speed of comet  = 6.0*10^4 ms

[tex]\Delta V = \frac{2m}{M+m} v[/tex]

[tex]\Delta V = \frac{2*4.0*10^12*6.0*10^4}{4.0*10^12+1.9*10^27}[/tex]

[tex]\Delta V = 6.3*10^{-11} m/[/tex]s

The change is VERY small, about [tex]10^{-11} m/s[/tex].

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