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An apple is dropped from rest at a height of 10 meters. Its vertical position, \(y(t)\), is governed by the second-order differential equation:$$\frac{d^2 y}{dt^2}=-g$$where \(g\) is the constant of gravitational acceleration.
  1. State the initial conditions for position \(y(0)\) and velocity \(y'(0)\).
  2. Verify that the general solution to this equation is \(y(t) = -\frac{1}{2}gt^2 + At + B\).
  3. Use the initial conditions to find the particular solution for the apple's motion.

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