Solution:
By conservation of energy, \(v_{\infty} = \sqrt{v^2 - v_{\text{esc}}^2} = \sqrt{(2v_{\text{esc}})^2 - v_{\text{esc}}^2} = v_{\text{esc}}\sqrt{3} = 11.2\sqrt{3} \text{km/s}\).
By conservation of energy, \(v_{\infty} = \sqrt{v^2 - v_{\text{esc}}^2} = \sqrt{(2v_{\text{esc}})^2 - v_{\text{esc}}^2} = v_{\text{esc}}\sqrt{3} = 11.2\sqrt{3} \text{km/s}\).
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