[Steps Shown] The velocity v of an object t seconds after it has been dropped from a height about the surface of the earth is given by the equation v = 32t
Question: The velocity v of an object t seconds after it has been dropped from a height about the surface of the earth is given by the equation v = 32t feet per second, assuming no air resistance. If we assume that air resistance is proportional to the square of the velocity, then the velocity after t seconds is given by the following equation.
\[v=100\left( \frac{{{e}^{0.64t}}-1}{{{e}^{0.64t}}+1} \right)\]- In how many seconds will the velocity be 50 feet per second?
- Can an object reach a velocity of 100 feet per second? Show work to justify or explain your answer.
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