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You stand at the top of a deep well
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 water hits the water's surface. The splash arrives 4.2 s after you drop the rock. The speed of sound in the well is Vs =331 m/s. Otheexpertta.com 50% Part Find the quadratic equation for the distance, D in terms of the time, the acceleration due to gravity, and the speed of sound, a Arrange the expression so that the coefficient of the D term is 1 50% Part (b) Solve the quadratic equation for the depth of the well, D, in meters.
Expert Solution
along vertical
for the sound
D = Vs*t1
time takne for sound to travell from well to top t1 = D/Vs = D/vs
for stone
initial velocity voy = 0
acceleration ay = -g
displacement y = -D
time taken t2 = t - t1 = t - D/vs
from equation of motion
y = voy*t2 + (1/2)*a*t2^2
-D = 0 - (1/2)*g*(t-D/vs)^2
D = (1/2)*g*(t^2 + D^2/(vs)^2 - 2*t*D/vs)
2D/g = t^2 + D^2/(vs)^2 - 2t*D/vs
D^2 - 2*t*D*vs + (vs*t)^2 - 2D*vs^2/g = 0
part(b)
D^2 - 2*4.2*D*331 + (331*4.2)^2 - 2*D*331^2/9.8 = 0
D = 77.11 m <<<-----------ANSWER
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