Ok, theres a differential equation that is:(adsbygoogle = window.adsbygoogle || []).push({});

dv/dt = 9.8 - (v/5), v(0) = 0

to represent a falling object. So the solution ends up being

v = 49(1 - e^t/5)

and the equilibrium solution (terminal velocity) is v = 49.

Now I have a problem that says "find the time that must elapse for the object to reach 98% of its limiting velocity"

To do this, I am doing the following:

terminal velocity * 98% = the equation...

49 * 0.98 = 49(1 - e^t/5)

div by 49...

0.98 = 1 - e^t/5

move 1 over and multiply both sides by -1...

1 - 0.98 = e^t/5

use ln...

ln(1 - 0.98) = t/5

mult by 5...

5 * ln(1 - 0.98) = t

so:

t = -19.56

now... in the book's solution, it states:

T = 5 * ln(50) ~= 19.56

So, where is this 50 coming from? And my answer looks to be right except for the sign, where did I go wrong?

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# Physics type math problem

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