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shutvik [7]
2 years ago
8

Please help me with the below question.

Mathematics
1 answer:
Romashka [77]2 years ago
5 0

By applying <em>algebraic</em> handling, <em>exponential</em> and <em>logarithm</em> properties, we conclude that the equation of the time of flight (T) is T = -\frac{1}{k}\cdot \ln \frac{\frac{g}{k} }{v_{o}+\frac{g}{k} }.

<h3>How to clear a variable within an exponential equation </h3>

In this question we must clear the variable of time of flight (T) by means of <em>algebraic</em> procedures. <em>Exponential</em> expressions are <em>trascendental</em> functions, these are, expressions that cannot be described algebraically:

v_{o}\cdot e^{-k\cdot T} - \frac{g}{k} \cdot (1 - e^{-k\cdot T}) = 0      

\left(v_{o} + \frac{g}{k} \right)\cdot e^{-k \cdot T} = \frac{g}{k}

e^{-k\cdot T} = \frac{\frac{g}{k} }{v_{o}+\frac{g}{k} }

- k\cdot T = \ln \frac{\frac{g}{k} }{v_{o}+\frac{g}{k} }

T = -\frac{1}{k}\cdot \ln \frac{\frac{g}{k} }{v_{o}+\frac{g}{k} }

By applying <em>algebraic</em> handling, <em>exponential</em> and <em>logarithm</em> properties, we conclude that the equation of the time of flight (T) is T = -\frac{1}{k}\cdot \ln \frac{\frac{g}{k} }{v_{o}+\frac{g}{k} }.

To learn more on exponential functions: brainly.com/question/11487261

#SPJ1

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