Escape speed (10-10)
Question 1 of 4
Question
Speed that a projectile must have at Earth’s surface in order to escape Earth.
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Review
The initial speed \(v_i\) for which Equation 10-9 is true is called the escape speed, which we denote by the symbol \(v_{\mathrm{escape}}\) . This is the minimum speed at which an object must be launched from Earth’s surface to escape to infinity. To find its value, replace \(v_i\) in Equation 10-9 with \(v_{\mathrm{escape}}\), add \(Gm_{\mathrm{Earth}}m/R_{\mathrm{Earth}}\) to both sides and multiply both sides by \(2/m\).
\(\frac{1}{2}mv_{\mathrm{escape}}^2 = \frac{Gm_{\mathrm{Earth}}m}{R_{\mathrm{Earth}}}\)
\(v_{\mathrm{escape}}^2 = \frac{2Gm_{\mathrm{Earth}}}{R_{\mathrm{Earth}}}\)
Finally, take the square root of both sides:
