Question 1061683: Im having problems with a discussion board question and need help. this is for Math 111 and I am completely lost. the question is as followed:
If we assume that air resistance is proportional to the square of the velocity, then the time t in seconds required for an object to reach a velocity v in feet per second is given by:
t=9/24ln 24+v/24-v, 0 ≤ v < 24
determine the velocity, to the nearest hundredth foot per second of the object after 1.3 seconds
Found 2 solutions by stanbon, Boreal:
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! If we assume that air resistance is proportional to the square of the velocity, then the time t in seconds required for an object to reach a velocity v in feet per second is given by:
t=9/24ln 24+v/24-v, 0 ≤ v < 24
determine the velocity, to the nearest hundredth foot per second of the object after 1.3 seconds
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Solve::
1.3 = (9/24)ln(24+v)/(24-v)
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ln[(24+v)/(24-v)] = 3.467
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(24+v)/(24-v) = e^3.467
24+v = 32.03(24-v)
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24+v = 768.72 - 32.03v
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33.03v = 744.72
v = 22.55
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Cheers,
Stan H.
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Answer by Boreal(15235)  (Show Source):
You can put this solution on YOUR website! If I assume it is 9/(24ln24); if it is (9/24)ln 24, then the first term is 1.192
That is 3/(8 ln 24)
That equals 0.1180
1.3=0.1180+v/24-v
1.182=v/24-v
multiply by 24 both sides
28.368=v-24v
-23v=28.368
v=-1.23 ft/sec. This is negative, which could be allowed since the velocity is downward, but it is too slow. So, let me look at the last term as v/(24-v)
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If the last term is (v/(24-v))
Then 1.182=v/(24-v)
multiply through by (24-v)
28.368-1.182v=v
28.368=2.182v
v=13.00 ft/sec, a positive result and one that makes sense given the velocity of a falling object is without friction 16 ft/sec.
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