Question

A stone is dropped into a well. The sound of the splash is heard 4.80 s later. What is the depth of the well? (Take the speed of sound to be 343 m/s.)

Answer 1

V = 343 m/s The total time taken by the stone to strike the well and the time taken by the sound to come up is, t + t, = 4.8 s Rearrange the above equation for tą, tz = (4.8 s-t1) ...... (1) Let the depth of the well be d. The distance travelled by the stone to strike the bottom point of the well is, d=ut, +18 Here, t, is the time taken by the stone to strike the bottom point of the well. The initial speed of the stone is zero as it is a free fall, that is, u=0 Therefore, the equation (2) becomes as follows, d=(0)6+- ...... (3) The sound of flash has constant velocity, therefore, the distance travelled up by the sound flash is, d=v_tz ...... (4) Here, v. is the velocity of the sound and t, is the time taken by the sound to travelled from bottom to top of the well. Equate the equations (3) and (4). 5gt = v.12 Substitute equation (1) in above equation.

18t1 =v. (4.8 s-1) Substitute the values in above equation. n/s) t =(343 m/s) (4.8 s-4) (4.9 m/s> ) t =(343 m/s)(4.8 st) t =(70 s)(4.8 s-t) ti = (336 s>) -(70 s) t +(70) t-(336) = 0 The solution of the above quadratic equation is, t = -74.5 s (or) 4.5 s Here, -74.5 is invalid time. Therefore, the time taken by the stone to reach the bottom point of the well is, t = 4.5 s Substitute 4.5 s for t, in above equation (2). = }(9.81 m/s?)(4.5 p.) = 99.32 m Therefore, the depth of the well is 99.32 m.