Problem: A stone is dropped into a well and the report of the stone striking the bottom is heard 7.7 seconds after it is dropped. Assume that the stone falls 16t2 feet in t seconds and that the velocity of sound is 1,120 feet per second. The depth of the well is:
Answer Choices:
A. 784 ft.
B. 342 ft.
C. 1568 ft.
D. 156.8 ft.
E. none of these
Solution:
Since the distance d traveled by the stone and the sound is the same, d=r1t1=r2t2. ∴ The times of travel are inversely proportional to the rates of fall: r1/r2=t2/t1.
∴112016t2/t=t7.7−t;∴t=7 (seconds); ∴16t2=16⋅72=784 (feet).