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

1. M = 67,422,800,892,977.54 kg

2. r = 15 km

Explanation:

The diameter of the Comet Tempel 1, D = 9.0 km across

The speed with which the dust escapes = 1.0 m/s

1. The escape velocity, , is given by the following formula

Where;

G = The universal gravitational constant = 6.67430 × 10⁻¹¹ N·m²/kg²

= The escape velocity of the debris = 1.0 m/s

M = The mass of the comet from where the debris escapes

From the escape velocity equation, we have;

Plugging in the values for the variables, we get the mass of the comet, 'M', as follows;

The mass of the comet, M ≈ 67,422,800,892,977.54 kg

2. When the debris has lost 60% of its initial kinetic energy, we have;

When the debris has lost 60% of its initial kinetic energy, the distance the debris will be from the comet's center, r = 15,000 m = 15 km