When an object is thrown straight up into the air, Newton's Second Law of Motion states that its height s (t) at time t is given by
S(t) = s0 + v0t + 1/2gt2
where v0 is its initial velocity and g is the constant of acceleration due to gravity. Suppose we take the measurements shown in Table 7.6.

(a) Find the least squares approximating quadratic for these data.
(h) Estimate the height at which the object was released (in m), its initial velocity (in m/s), and its acceleration due to gravity (in m/s2).
(c) Approximately when will the object hit the ground?

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Table 7.6 Time (s) Height (m) 0.5 5 23 7 2 23 18