Respuesta :
Answer:
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, [tex]v_e[/tex], is given by the following formula
[tex]v_e = \sqrt{\dfrac{2 \cdot G \cdot M}{R} }[/tex]
Where;
G = The universal gravitational constant = 6.67430 × 10⁻¹¹ N·m²/kg²
[tex]v_e[/tex] = 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;
[tex]M = \dfrac{v_e^2 \cdot R}{2 \cdot G}[/tex]
Plugging in the values for the variables, we get the mass of the comet, 'M', as follows;
[tex]M = \dfrac{1.0^2 \times 9,000}{2 \cdot 6.67430 \times 10^{-11}} \approx 67,422,800,892,977.54 \, kg[/tex]
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;
[tex]60\% \, K.E. = 0.6\cdot K.E. = 0.6 \times \dfrac{1}{2} \times m \times v_e^2 = \dfrac{G \cdot M \cdot m}{r}[/tex]
[tex]\therefore \, The \ distance \ of \ debris \ from \ the \ center, \, r = \dfrac{G \cdot M }{0.6 \times \dfrac{1}{2} \times v_e^2 }[/tex]
[tex]r = \dfrac{6.67430 \times 10^{-11} \times 67,422,800,892,977.54}{0.6 \times \dfrac{1}{2} \times 1^2 } = 15,000[/tex]
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
