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Imagine that you are standing at a wishing well, wishing that you knew how deep the surface of the water was. Cleverly, you make your wish. Then you take a penny from your pocket and drop it into the well. Exactly three seconds after you dropped the penny, you hear the sound it made when it struck the water. If the speed of sound is 343 m/s, how deep is the well? Neglect any effects due to air resistance. (Assume that the sound was heard exactly 3 s after the penny was dropped.)

Respuesta :

Answer:h=40.69 m

Explanation:

Given

after 3 s you heard the sound of coin

speed of sound=343 m/s

let h be the height of well

[tex]h=ut+\frac{gt_1^2}{2}[/tex]

[tex]t_1=\sqrt{\frac{2h}{g}}[/tex]

While coming back time taken

[tex]t_2=\frac{h}{343}[/tex]

[tex]t_1+t_2=3[/tex]

[tex]\sqrt{\frac{2h}{g}}+\frac{h}{343}=3[/tex]

[tex]h^2-26059.25h+9\times 343^2=0[/tex]

h=26018.554, 40.69 m

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