Answer:
58515.9 m/s
Explanation:
We are given that
[tex]d_1=4.7\times 10^{10} m[/tex]
[tex]v_i=9.5\times 10^4 m/s[/tex]
[tex]d_2=6\times 10^{12} m[/tex]
We have to find the speed (vf).
Work done by surrounding particles=W=0 Therefore, initial energy is equal to final energy.
[tex]K_i+U_i=K_f+U_f[/tex]
[tex]\frac{1}{2}mv^2_i-\frac{GmM}{d_1}=\frac{1}{2}mv^2_f-\frac{GmM}{d_2}[/tex]
[tex]\frac{1}{2}v^2_i-\frac{GM}{d_1}+\frac{GM}{d_2}=\frac{1}{2}v^2_f[/tex]
[tex]v^2_f=2(\frac{1}{2}v^2_i-\frac{GM}{d_1}+\frac{GM}{d_2})[/tex]
[tex]v_f=\sqrt{2(\frac{1}{2}v^2_i-\frac{GM}{d_1}+\frac{GM}{d_2})}[/tex]
Using the formula
[tex]v_f=\sqrt{v^2_i+2GM(\frac{1}{d_2}-\frac{1}{d_1})}[/tex]
[tex]v_f=\sqrt{(9.5\times 10^4)^2+2\times 6.7\times 10^{-11}\times 1.98\times 10^{30}(\frac{1}{6\times 10^{12}}-\frac{1}{4.7\times 10^{10})}[/tex]
Where mass of sun=[tex]M=1.98\times 10^{30} kg[/tex]
[tex]G=6.7\times 10^{-11}[/tex]
[tex]v_f=58515.9 m/s[/tex]
