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Even though Alice visits the wishing well frequently and always tosses in a coin for good luck, none of her wishes have come true. As a result, she decides to change her strategy and make a more emphatic statement by throwing the coin downward into the well. If the water is 7.03 m below the point of release and she hears the splash 0.81 seconds later, determine the initial speed at which she threw the coin. (Take the speed of sound to be 343 m/s.)

Respuesta :

Explanation:

The formula to calculate total time taken is as follows.

      Total time = time to fall + time for sound

So,   time for sound = [tex]\frac{distance}{velocity}[/tex]

                                 = [tex]\frac{7.03}{343}[/tex]

                                 = 0.0204  sec

Hence, time to fall is as follows.

          (0.81 - 0.0204) sec

         = 0.7896 sec

Now, we will calculate the time to fall as follows.  

            y = [tex]y_{o} + v_{o}yt + \frac{1}{2}at^{2}[/tex]

            0 = [tex]h + v \times t - \frac{1}{2}gt^{2}[/tex]

            0 = [tex]7.03 + v \times (0.81 - 0.0204) - 0.5 \times 9.81 \times(0.81 - 0.0204)^{2}[/tex]

               = [tex]7.8196 - 0.5 \times 9.81 \times 0.623[/tex]

              = 7.8196 - 3.058

              = 4.7616 m/s  

Therefore, she threw the coin at 4.76 m/s in the upward direction.

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