On July 4, 2005, the NASA spacecraft Deep Impact fired a projectile onto the sur

Question

On July 4, 2005, the NASA spacecraft Deep Impact fired a projectile onto the surface of Comet Tempel 1. This comet is about 9.0 km across. Observations of surface debris released by the impact showed that dust with a speed as low as 1.0 m/s was able to escape the comet.

1. Assuming a spherical shape, what is the mass of this comet? ( The escape speed for an object at the surface of Earth is 11.2 km/s).

Express your answer using two significant figures.
M =     kg



2. How far from the comet's center will this debris be when it has lost 60% of its initial kinetic energy at the surface?

Express your answer using two significant figures.
r =      km

Explanation / Answer

V escape = SQRT(2*G*m/r), where G is the gravitational constant,

 m is the mass of the comet, and r is the radius of the comet.

V e = SQRT{(2*6.6*10^-11*m)/4500}
V e = 1 m/s as given by the question
1 = SQRT{(13.2*10^-11*m)/4500}
4500 = 13.2*10^-11*m
m= 3.4*10^13 kg

60% of the kinetic energy = 0.6*0.5*m*v^2 = mgh, where h is altitude

 of the debris above the surface of the comet.
h = 106 meter above the surface or 4500+106 =4606 meters!
(This part of your question is not clear. I hope the calculation I made will meet your satisfaction!)

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