A rock is dropped into a well and the distance traveled is 16 t 2 feet, where t is the time. If the water splash is heard 3 seconds after the rock was dropped, and that the speed of sound is 1100 ft / sec, approximate the height of the well Choose one:
A) 134.8 feet
B) 136.2 feet
C) 132.7 feet
D) 132.2 feet
E) 115.3 feet

Rationale: let t 1 be the time it takes the rock to reach the bottom of the well . if h is the height of the well , we can write h = 16 t 1 2 let t 2 be the time it takes sound wave to reach the top of the well . we can write h = 1100 t 2 the relationship between t 1 and t 2 is t 1 + t 2 = 3 eliminate h and combine the equations h = 16 t 1 2 and h = 1100 t 2 to obtain 16 t 1 2 = 1100 t 2 we now substitute t 2 by 3 - t 1 in the above equation 16 t 1 2 = 1100 ( 3 - t 1 ) the above is a quadratic equation that may be written as 16 t 1 2 + 1100 t 1 - 3300 = 0 the above equations has two solutions and only one of them is positive and is given by t 1 = 2.88 seconds ( 2 decimal places ) we now calculate the height h of the well h = 16 t 1 2 = 16 ( 2.88 ) 2 = 132.7 feet answer c
Answer: C