48 ANSWERS TO PRACTICAL 



(Key, p. 34, Prob. n.) The method adopted in solving 

 this problem is merely the rough one in common use, and 

 gives only an approximate result. If an exact answer is de- 

 sired, we should take in account the time required for the sound 

 to reach the ear. The following method may be employed : 



aj = No. sec. for stone to fall. 

 4 a = " " sound to reach the ear. 

 16x 2 = (4 a:)1090. 

 16a; a = 4360 1090a;. 



From this, by completing the square, we have 



a = 3.7892+ seconds. 

 Then the equation (2) d = i6/ 2 gives the depth. 



d = 16(3.7892 +) 2 = 229 ft. and 8.795 in., 

 which is the answer exact within a small fraction. 

 A second method (more exact) 



d = depth of the well = 16i a . 



4 i y/d = No. of sec. for sound to reach the eftZ. 

 (4 -i v/d)l090 =4360 - 



_ __ 190Q8SOC. 



