Question

You stand at the top of a deep well. To determine the depth, D, of the well you drop a rock from the top of the well and listen for the splash as the rock hits the water’s surface. The sound of the splash arrives t = 4.3 s after you drop the rock. The speed of sound in the well is v_s = 336 m/s

(7%) Problem 6: You stand at the top of a deep well. To determine the depth, D, of the well you drop a rock from the top of the well and listen for the splash as the rock hits the water's surface. The sound of the splash arrives t = 4.3 s after you drop the rock. The speed of sound in the well is vs = 336 m/s. Otheexpertta.com @theexpertta.com - tracking id: 1F76-4D-OF-4B-8D79-19495. In accordance with Expert TA's Terms of Service.copying this information to any solutions sharing website is strictly forbidden. Doing so may result in termination of your Expert TA Account. 50% Part (a) Enter the quadratic equation for the distance, D, in terms of the time, the acceleration due to gravity, and the speed of sound. Arrange the expression so that the coefficient of the D2 term is 1. O=D2 - 2 vstD-2 v 2D/g + t2 v2 Correct! 50% Part (b) Solve the quadratic equation for the depth of the well, D, and calculate it's value, in meters. D=1 Grade Summary Deductions 9% Potential 91%

Answer 1

Ans @ Time taken by the rock to hit the surface of earth well is t , which is calculated as. ħ from the equation y=Uy t +1 agt -D=0xt-Źg th =) t, - VZD and time taken by sound to reach top surface is D Us But total time, t = 6 + tz ta= nalo * 1 + 1 + 2 + y = 2 Vå g ttg D² - 2tg DV = 2D V5 on dividing by g' we get lut ² + D2 - 1 2 ED_QDV6=0 of g - 0 but t= 4.38, ve z 336m/s, g = 9.8 m/s² Substitute all these values in equm , we get

= D - 2 X(336x4-3 D-2 (336) D +(4.3) (336) to - D² - 2889.6D-23040D+20874470 - D² - 25926-6D+2087447 -0. axt batct-o 3 for a Quadratic Equation then n=nbt v62_4ac 29 .:D = -(-2592616) I V (= 259 26:63²4 X1 X 2 087447 D = 2592606 I v 66 3838600 2 =) D=25 g 26.6 1 25765.0694 2 negative taking only the positive value we get =) D = 25926.6-25765= 161·53 meters D = 80.76 metery Ang