In this problem, we're going to use the equation of motion:

$\overline{){\mathbf{\u2206}}{\mathbf{y}}{\mathbf{=}}{{\mathbf{v}}}_{\mathbf{0}\mathbf{y}}{\mathbf{t}}{\mathbf{+}}\frac{\mathbf{1}}{\mathbf{2}}{\mathbf{a}}{{\mathbf{t}}}^{{\mathbf{2}}}}$

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 water hits the water’s surface. The splash arrives t = 4.2 s after you drop the rock. The speed of sound in the well is v_{s} = 331 m/s

Part (a) Find 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 D^{2} term is 1.

Part (b) Solve the quadratic equation for the depth of the well, D, in meters.

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What scientific concept do you need to know in order to solve this problem?

Our tutors have indicated that to solve this problem you will need to apply the Kinematics Equations concept. You can view video lessons to learn Kinematics Equations. Or if you need more Kinematics Equations practice, you can also practice Kinematics Equations practice problems.