Accounting for Air Resistance

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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