Giancoli 7th Edition textbook cover
Giancoli's Physics: Principles with Applications, 7th Edition
Describing Motion: Kinematics in One Dimension
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2-1 to 2-3: Speed and Velocity
2-4: Acceleration
2-5 and 2-6: Motion at Constant Acceleration
2-7: Freely Falling Objects
2-8: Graphical Analysis

Question by Giancoli, Douglas C., Physics: Principles with Applications, 7th Ed., ©2014, Reprinted by permission of Pearson Education Inc., New York.
Problem 6

According to a rule-of-thumb, each five seconds between a lightning flash and the following thunder gives the distance to the flash in miles.

  1. Assuming that the flash of light arrives in essentially no time at all, estimate the speed of sound in m/s from this rule.
  2. What would be the rule for kilometers?
  1. 3×102 m/s3\times10^2\textrm{ m/s}
  2. 1 km for every 3 sec.1\textrm{ km for every }3\textrm{ sec.}
Giancoli 7th Edition, Chapter 2, Problem 6 solution video poster

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This is Giancoli Answers with Mr. Dychko. When this question says that you can assume the light arrives in essentially no time at all, what they are saying is that when you see the flash of lightning, that is the same moment at which the sound is produced by the lightning, the thunder, in other words and it's a really good assumption because lightning travels so fast it's the fastest thing around—3 times 10 to the 8 meters per second. So we can calculate the speed of sound then and we have the 1 mile for every 5 seconds is our rule of thumb and we'll convert that into meters per seconds by multiplying by 1610 meters for every mile and so the miles cancel giving us 322 meters per second; I guess I can plug that into the calculator here if you wanna see it. And since it's just a rule of thumb, only one significant figure is appropriate so we will have 3 times 10 to the 2 meters per second is gonna be our calculation for the speed of sound. Another rule of thumb for kilometers well, we'll have to figure out how long it will take for for the sound to travel 1 kilometer. So we know that distance is gonna be 1 kilometer because our rule of thumb is how long does it take for sound to travel one unit of distance; 1 mile up here or now we are gonna say 1 kilometer. So we have this kilometer divided by the speed of sound which is 322 meters per second, as we calculated up here, and multiply that by 1 kilometer for every 1000 meters so that we get rid of the meters in the bottom and have kilometers there instead so that these kilometers here cancel and we end up with seconds because this is 1 over 1 over seconds after you get rid of all the distance units and that's the same as 1 multiplied by the reciprocal of the denominator which is seconds over 1— hopefully I haven't confused you by saying all of that but anyway. So you end up with 3.1 seconds and so the rule of thumb is the lightning is 1 kilometer away for every 3 seconds that you count between the flash of light and hearing the thunder.

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