Bill and Ben are on a bridge, timing how long it takes stones they have dropped to hit the water below. A quadratic relation can be used to determine the distance, D, in metres, that ta stone will fall in the time, t, in seconds after it is realeased. In this relation, a = -0.5g, where g is acceleration due to gravity, which is approximately 9.8 m/s2 on Earth. Ben starts a timer when Bill releases a stone, and he stops the timer when the stone hits the water below. The mean time of serveral trials is 3 s.
a) Determine a quadratic function that models the falling stones.
b) How high above the water are Bill and Ben? Explain your answer.
c) On Saturn's moon, Titan, the value of g is 1.35 m/s2. Suppose that Bill and Ben are astronauts and they are standing at the top of a cliff on Titan. If they record the time for a stone to fall from their hands to the bottom of the cliff as 3 s, how high is the cliff, to the nearest hundreth of a metre?