(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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.

How far from the comet's center will this debris be when it has lost 90 % of its initial kinetic energy at the surface?

2. Relevant equations

3. The attempt at a solution

The equation for escape velocity can help determine the mass: 1.0 m/s = sqrt((2*G*M)/4500 m), M = 3.4 x 10^13.

KE at the surface = (1/2)(3.4 x 10^13)(1.0)^2 = 1.7 x 10^13 -- 90% of that is 1.53 x 10^13 J. So 90% of the kinetic energy has been converted into potential energy, right? Potential energy is (GMm)/r... but then I have two unknowns (m & r). How do I solve this? Is there another equation that can make the m cancel?

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# Homework Help: Mass/escape velocity of a comet

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