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Velocity–Altitude Equation for Freefall with Variable Gravity

Physics · Physics — University

Course: Physics Book: Physics — University

Question

Accounting for the variation of gravitational acceleration $a$ with respect to altitude $y$, derive an equation that relates the velocity of a freely falling particle to its altitude. Assume the particle is released from rest at altitude $y_0$ above Earth's surface. With what velocity does the particle strike Earth if it is released from rest at $y_0 = 500\text{ km}$? Use $g = 9.81\text{ m/s}^2$ and $R = 6371\text{ km}$.

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