The distance to the surface of the water in a well can sometimes be found by dropping an object into the well and measuring the time elapsed until a sound is heard. if
t 1t1
is the time (in seconds) it takes for the object to strike thewater, then
t 1t1
obeys the equation
s equals 16 t subscript 1 superscript 2s=16t21,
where s is the distance (in feet). solving for
t 1t1,
we have
t 1 equals startroot s endroot divided by 4t1=s/4.
let
t 2t2
be the time it takes for the sound of the impact to reach your ears. since sound waves travel at a speed of approximately 1100 feet per second, the time to travel the distance s is
t 2 equals s divided by 1100.t2=s/1100.  
now
t 1 plus t 2t1+t2
is the total time that elapses from the moment that the object is dropped to the moment that a sound is heard. we have the equation
total elapsed time equals t 1 plus t 2 equals startfraction startroot s endroot over 4 endfraction plus startfraction s over 1100 endfraction