anonymous
  • anonymous
A stone is dropped from the top of a cliff. The splash it makes when striking the water below is heard 2.0s later. How high is the cliff?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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Jack1
  • Jack1
|dw:1378611094682:dw|
Jack1
  • Jack1
s = ut + (1/2)at^2
Jack1
  • Jack1
distance = s = ? initial velocity = u = 0 (dropped, not thrown) t = time = 2 (seconds) a = acceleration = gravity = 9.8 m/s^2

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Jack1
  • Jack1
can you solve from here @Autumn0909 ?
anonymous
  • anonymous
I got that but that is only the time it takes down, the sound has to travel back up the distance to be heard.
Jack1
  • Jack1
ok so what's the speed of sound that you're using?
Jack1
  • Jack1
340.3 m/s ish?
anonymous
  • anonymous
I got |dw:1378611463385:dw| but I don't know where to go from there
anonymous
  • anonymous
speed of sound is not given, my teacher uses 343m/s but I think masteringphysics uses 340m/s
Jack1
  • Jack1
so adapting this eqn to account for speed of sound: s = ut + (1/2)at^2 --> s = ut + 1/2 a (t - s/v)^2 so u = 0 therefore s = 1/2 a (t - s/v)^2 and s = ? t = 2 a = g = 9.8 v = 340 so:
anonymous
  • anonymous
\[d=vi*t+\frac{1}{2}at^2\] where initial velocity is zero so we have d =distance a=acceleration=gravity=9/8m/s^2 t=times=2 seconds \[d=\frac{1}{2}(9.8 \frac{m}{s^2} {}2 s^2)\] \[d=\frac{1}{2}(9.8 \frac{m}{s^2} {}4 s^2)\] \[d=\frac{1}{2}(9.8 * 4 m )\]units cancels simplify the rest
Jack1
  • Jack1
(t - s/v)^2 = (2 - s/340)^2 =(2 - s/340)(2 - s/340) expanding out using foil = s^2 / 115600 - s/85 +4
Jack1
  • Jack1
therefore: s = 1/2 x G x (s^2 / 115600 - s/85 +4) s = 1/2 x 9.8 x (s^2 / 115600 - s/85 +4) s = 4.9 x (s^2 / 115600 - s/85 +4) heres where it getts a bit messy s = 0.0000423875s^2 - 0.0576471s + 19.6 0 = 0.0000423875s^2 - 0.0576471s + 19.6 - s 0 = 0.0000423875s^2 - 1.0576471s + 19.6 now solve using quadratic equation solution should give you 2 answers for s
Jack1
  • Jack1
only one will be a reasonable answer tho, the other will be around 25000m and can be ignored
anonymous
  • anonymous
the answer is supposed to be two significant figures...
Jack1
  • Jack1
how'd u go? also, quadratic formula below if u need refresher
Jack1
  • Jack1
so a = 0.0000423875 b = -1.0576471 and c = 19.6
anonymous
  • anonymous
and i got two positive numbers
Jack1
  • Jack1
yep what are they?
Jack1
  • Jack1
you should get s = 24934 m or s = 18.55 m
anonymous
  • anonymous
ok I made a mistake the first time I did it, I got those numbers now
Jack1
  • Jack1
and it's unlikely that you'd be standing on a cliff 25 km vertical height so: answer is num 2
anonymous
  • anonymous
Ah thank you so much, it was the foiling that got me :)
Jack1
  • Jack1
all good happy to help hay slaters and happy weekend!

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