SOLUTION: 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 give

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Question 1061689: 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
Answer by ikleyn(52817) About Me  (Show Source):
You can put this solution on YOUR website!
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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
~~~~~~~~~~~~~~~~~~~~~~~~~ 

If your formula is

t = %289%2F24%29%2Aln%28%2824%2Bv%29%2F%2824-v%29%29 


then they want you to solve this equation for "v":

1.3 = %289%2F24%29%2Aln%28%2824%2Bv%29%2F%2824-v%29%29.


It is equivalent to

1.3%2A%2824%2F9%29 = ln%28%2824%2Bv%29%2F%2824-v%29%29    or

ln%28%2824%2Bv%29%2F%2824-v%29%29 = 3.4666,

%2824%2Bv%29%2F%2824-v%29 = e%5E3.4666%29,

%2824%2Bv%29%2F%2824-v%29 = 2.71828%5E3.4666,

%2824%2Bv%29%2F%2824-v%29 = 32.03   (approximately).


====> 24 + v = 32.03*(24 - v)  ====>  v + 32.03v = 32.03*24 - 24  ====>  v = 744.72%2F%281%2B32.03%29 = 22.55  (approximately).

Solved. The answer is v = 22.55.

Check. %289%2F24%29%2Aln%28%2824%2B22.55%29%2F%2824-22.55%29%29 = 1.3. Correct !