Distance Traveled

Question

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 T1 is the time
(measured in seconds) that it takes for the object to strike the water, then T1 obeys the equation: s=16(T1)^2 where s is the distance (measured in feet). Solving for T1, we have T1=(sqrt of s)/4. Let T2 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 T2=s/1100. Now T1+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: T1+T2=(sqrt of s)/4+s/1100.

Find the distance to the waters surface if the total time elapsed from dropping a rock to hearing it hit water is 1.0 seconds. s is equal to how many feet?

Answer 1

1= (sqr(s))/4 + s/1100

solve for s

= about 15.9 feet

graph it, find the x intercept

use a graphing calculator

or do the algebra but check for an extraneous root