Physics: Using Sound to Measure Distance The distance to the surface of the water in a wel...

Physics: Using Sound to Measure Distance 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 will obey the equation where s is the distance (measured in feet). It follows that . Suppose that t2 is the time that it takes for the sound of the impact to reach your ears. Because sound travels at a speed of approximately 1100 feet per second, the time t2 for the sound to travel the distances will be . See the illustration on the following page. 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

Find the distance to the water’s surface if the total time elapsed from dropping a rock to hearing it hit water is 4 seconds.