An object with mass \(m = 1 \text{ kg}\) is launched straight upwards from ground level with initial velocity \(v_0 = 100 \text{ m/s}\). While it is moving upward, the net force on the object from gravity and from air resistance is \[F = -mg - \frac{v^2}{100}. \] In the equation above, the negative signs indicate that the forces oppose the motion. The gravitational acceleration \(g\) is \(10 \text{ m/s}^{2}\), and \(v\) is the instantaneous velocity in the vertical direction.

To the nearest meter, what height (relative to ground) does the object reach before it begins to fall back down?

**Note:** Assume that the scaling factor on the \(v^2\) term has the units required for that term to represent force.

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