(20%) Problem 2: You stand at the top of a deep well. To determine the depth, D,

Question

(20%) Problem 2: 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.I s after you drop the rock. The speed of sound in the well is Vs-330 m/s ©theexpertta p, ? 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 s Arrange the expression so that the coefficient of the D2 term is 1 Grade Summar Deductions Potential Submissions Attempts remain (5% per attempt detailed view 123 0 END BACKSPACE I DELI CLEAR Submit Hint I give up! Hints: 1% deduction per hint. Hints remaining: 2 Feedback: 1% deduction per feedback ? 50% Part (b) Solve the quadratic equation for the depth of the well, D, and calculate it's value, in meters

Explanation / Answer

According to the question

t = 4.1 s

vs = 330 m/s

Put the values in using formula

S = ut + 1/2 at^2

D = 1/2 g t^2

v = D/T => D = vT = 330T

2D = 0.5 x 9.8 t^2 + 330 T

T = 4.1 - t

2D = 4.9t^2 + 330 (4.1 - t)

2D = 4.9t^2 +1353 - 330 t

4.9t^2 - 330 t + 1353 = 2D

D = 2.45 t^2 - 165t + 676.5

Then,

D = 1/2 g t^2 = 4.9 t^2

4.9t^2 - 2.45 t^2 + 165 t - 676.5 = 0

2.45 t^2 + 165 t - 676.5 = 0

the above quadratic eqn will give us

t = 3.87 s

D = 4.9 x 3.87^2 = 73.39 m ;

Hence,

D = 73.39 m

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