Dropping rocks on other planets: 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,...

Dropping rocks on other planets: 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 2 seconds to 6 seconds into the drop? (Hint: This question may be rephrased as follows: “If time increases by a factor of 3, by what factor will distance increase?”)

b. For objects falling near the surface of Mars, if time is measured in seconds and distance in feet, the value of c is 6.4. If a rock is dropped from 70 feet above the surface of Mars, how long will it take for the rock to strike the ground?

c. On Venus, a rock dropped from 70 feet above the surface takes 2.2 seconds to strike the ground. What is the value of c for Venus?