Standing On The Shoulders Of Giants - Time Taken To Fall

Calculus Level 2

By recreating Galileo's famous Leaning Tower of Pisa experiment, we obtained the following table of data which indicates the vertical height \(h\) that the cannonballs dropped \(t\) seconds after being released till it hits the ground and comes to rest.

time \(t\)012345
height \( h \)0519445656

Which of the following is the best approximation for the time taken for the cannonballs to reach the ground?

Image credit: Wikipedia F l a n k e r

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