# 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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