An experiment to measure the value of g is constructed using a tall tower outfitted with two sensing devices, one a distance H above the other. A small ball is fired straight up in the tower so that it rises to near the top and then falls back down; each sensing device reads out the time that elapses between the ball going up past the sensor and back down past the sensor.
(a) It takes a time 2t1 for the ball to rise past and then come back down past the lower sensor, and a time 2t2 for the ball to rise past and then come back down past the upper sensor. Find an expression for g using these times and the height H. (Use the following as necessary: t1, t2, and H.)
(b) Determine the value of g if H equals 21 m, t1 equals 4 s, and t2 equals 3.42 s.