Predict/Calculate When you drop a rock into a well, you hear the splash 1.5 seconds later. (a) How deep is the well? (b) If the depth of the well were doubled, would the time required to hear the splash be greater than, less than, or equal to 3.0 seconds? Explain.
Cannot be hand-drawn, this physics HOMEWORK solution must be typed out, and the explanation in the simplest manner.
Teachers hint:
The distance for the stone to drop is of course the same as the distance for the sound to return. We are going going to get two simultaneous equations to solve for t1 and t2. t1 is the time for the stone to drop and t2 the time for the echo to return. We are given the total time is 1.5 seconds.
So set 1/2 g t1^2 = v t2 multiply by 2 to get: gt1^2 = 2v t2
then gt1^2 - 2v t2 = 0 equation 1
next: t1 + t2 = 1.5 seconds equation 2
solve simultaneously for either t1 or t2 then use t1 + t2 = 1.5 to get the other.
Carry out to 4 decimal places and round to 3. One value will be much higher than the other. Test each value of t in their respective equations for distance. The distances will be close.
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