Answer:
[tex]v_{f}=51109.88m/s[/tex]
Explanation:
Given data
At d₁=4.5×10¹⁰m the speed of comet is Vi=9.2×10⁴m/s
At d₂=6×10¹²m the speed will Vf
The work done by surrounding is zero and the energy of system at the initial state equal the energy at final state so we can apply:
[tex]E_{f}=E_{i}+W\\K_{f}+U_{f}=K_{i}+U_{i}+0\\1/2mv_{f}^{2}+\frac{-GMm}{d_{2}}=1/2mv_{i}^{2}+\frac{-GMm}{d_{i}} \\v_{f}=\sqrt{v_{i}^2+2GMm[1/d_{2}-1/d_{1}]}[/tex]
Substitute the given values to find final velocity Vf
So
[tex]v_{f}=\sqrt{(9.2*10^{4}m/s )^2+2(6.7*10^{-11})(1.98*10^{30})[1/6*10^{12}-1/4.5*10^{10}]} \\v_{f}=51109.88m/s[/tex]
