Accounting for Air Resistance

An object with mass m=1 kgm = 1 \text{ kg} is launched straight upwards from ground level with initial velocity v0=100 m/sv_0 = 100 \text{ m/s}. While it is moving upward, the net force on the object from gravity and from air resistance is F=mgv2100.F = -mg - \frac{v^2}{100}. In the equation above, the negative signs indicate that the forces oppose the motion. The gravitational acceleration gg is 10 m/s210 \text{ m/s}^{2}, and vv 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 v2v^2 term has the units required for that term to represent force.

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