Gravity Gradient

In standard kinematics problems involving gravity, we assume a constant gravitational field strength. Suppose instead that we have a fictitious scenario in which the gravity field strength varies as follows: g=g0+ky,g = g_0 + ky, where yy (in meters) is the distance above the ground. Here, the gravity is weakest at ground level and becomes stronger with increasing altitude (whilst always pointing toward the ground).

Consider the time tft_f (in seconds) that it would take for an object to fall from an initial resting height y0y_0 to the ground. To 2 decimal places, what is the limiting value of tft_f as y0y_0 approaches infinity?

Note: The quantity gg has units of m/s2\text{m/s}^2, g0=10 m/s2g_0 = 10 \text{ m/s}^2, and k=1/s2k= 1/\text{s}^{2}.

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