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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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5 : 4 10 : 8 15 : 12 20 : 16 25 : 20

30 : 24 35 : 28 40 : 32 45 : 36 50 : 40

55 : 44 60 : 48 65 : 52 70 : 56 75 : 60

80 : 64 85 : 68 90 : 72 95 : 76 100 : 80

105 : 84 110 : 88 115 : 92 120 : 96 125 : 100

130 : 104 135 : 108 140 : 112 145 : 116 150 : 120

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230 : 184 235 : 188 240 : 192 245 : 196 250 : 200

255 : 204 260 : 208 265 : 212 270 : 216 275 : 220

280 : 224 285 : 228 290 : 232 295 : 236 300 : 240

305 : 244 310 : 248 315 : 252 320 : 256 325 : 260

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380 : 304 385 : 308 390 : 312 395 : 316 400 : 320

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430 : 344 435 : 348 440 : 352 445 : 356 450 : 360

455 : 364 460 : 368 465 : 372 470 : 376 475 : 380

480 : 384 485 : 388 490 : 392 495 : 396 500 : 400

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