It is a consequence of Newton’s law of gravitation that near the surface of any planet, the distance D fallen by

Excerpt
near the surface of a planet. What is the comparison in distance fallen from 3 seconds to 12 seconds into the drop? ( nt: Ts question may be rephrased as follows: “If time increases by a factor of 4, by what factor will distance increase?”)

It is a consequence of Newton’s law of gravitation that near the surface of any planet, the distance D fallen by a rock in time t is given by D = ct 2 . That is, distance fallen is proportional to the square of the time, no matter what planet one may be on. But the value of c depends on the mass of the planet. For Earth, if time is measured in seconds and distance in feet, the value of c is 16. (a) Suppose a rock is falling near the surface of a planet. What is the comparison in distance fallen from 3 seconds to 12 seconds into the drop? ( nt: Ts question may be rephrased as follows: “If time increases by a factor of 4, by what factor will distance increase?”)

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