Answer:
Explanation:
From the given information:
Distance [tex]d_i = 4.8 \times 10^{10} \ m[/tex]
Speed of the comet [tex]V_i = 9.1 \times 10^{4} \ m/s[/tex]
At distance [tex]d_2 = 6 \times 10^{12} \ m[/tex]
where;
mass of the sun = [tex]1.98 \times 10^{30}[/tex]
[tex]G = 6.67 \times 10^{-11}[/tex]
To find the speed [tex]V_f[/tex]:
Using the formula:
[tex]E_f = E_i + W \\ \\ where; \ \ W = 0 \ \ \text{since work done by surrounding is zero (0)}[/tex]
[tex]E_f = E_i + 0 \\ \\ K_f + U_f = K_i + U_i \\ \\ = \dfrac{1}{2}mV_f^2 + \dfrac{-GMm}{d^2} = \dfrac{1}{2}mV_i^2+ \dfrac{-GMm}{d_i} \\ \\ V_f = \sqrt{V_i^2 + 2 GM \Big [ \dfrac{1}{d_2}- \dfrac{1}{d_i}\Big ]}[/tex]
[tex]V_f = \sqrt{(9.1 \times 10^{4})^2 + 2 (6.67\times 10^{-11}) *(1.98 * 10^{30} ) \Big [ \dfrac{1}{6*10^{12}}- \dfrac{1}{4.8*10^{10}}\Big ]}[/tex]
[tex]\mathbf{V_f =53.125 \times 10^4 \ m/s}[/tex]
