# Finding value for time from equation (DIFFICULT)

Find the time takes skydiver to hit the ground using th following:

y = (t/SQRT(10) - 2ln(1+e^(t/SQRT(10)) - C) x 20SQRT10

## The Attempt at a Solution

Have tried many times to find value for t with little success help needed!

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HallsofIvy
Homework Helper
Find the time takes skydiver to hit the ground using th following:

y = (t/SQRT(10) - 2ln(1+e^(t/SQRT(10)) - C) x 20SQRT10

## The Attempt at a Solution

Have tried many times to find value for t with little success help needed!
So you want to solve
$$20\sqrt{10}(\frac{t}{\sqrt{10}}- 2ln(1+ e^{\frac{t}{\sqrt{10}}})- C)= 0$$

I would start by doing two things: divide both sides by $20\sqrt{10}$ and replace $t/\sqrt{10}$ by "u". Now the equation is
$$u- 2ln(1+ e^u)- C= 0$$

Of course, you can't get a specific numerical result without a specic value for C. Even then I suspect that there will be no solution in terms of elementary functions.

Okay well I derived the solution stated from the following:

y' = 20SQRT10 x (1-e^(t/SQRT10))/(1+e(t/SQRT10))

Where C is a constant of integration, is this correct? Becasue the question looks as if a specific numerical value must be found.

Mark44
Mentor
Okay well I derived the solution stated from the following:

y' = 20SQRT10 x (1-e^(t/SQRT10))/(1+e(t/SQRT10))

Where C is a constant of integration, is this correct? Becasue the question looks as if a specific numerical value must be found.
Why would you take the derivative?

The skydiver will be on the ground at the time when y = 0 in the equation in your first post. That's what HallsOfIvy was telling you in his reply. Did you read it?

Since no integration has apparently been done, C is not a constant of integration. Is there any other information in your problem that you haven't posted?

Well in order to obtain the equation :

y = (t/SQRT(10) - 2ln(1+e^(t/SQRT(10)) - C) x 20SQRT10

I had to use seperation of variables and integration on the following:

y' = 20SQRT10 x (1-e^(t/SQRT10))/(1+e(t/SQRT10))

Which is the reason for the constant of integration C, try it yourself and see if you come up with the same solution as me. Only other information is that at y(0) = 4000.

Thanks

Mark44
Mentor
Well in order to obtain the equation :

y = (t/SQRT(10) - 2ln(1+e^(t/SQRT(10)) - C) x 20SQRT10

I had to use seperation of variables and integration on the following:

y' = 20SQRT10 x (1-e^(t/SQRT10))/(1+e(t/SQRT10))

Which is the reason for the constant of integration C, try it yourself and see if you come up with the same solution as me. Only other information is that at y(0) = 4000.

Thanks
There's a reason for the three parts in the problem template, of which the first is the complete problem statement and all pertinent data. As you presented the problem, there was no indication that you were solving a differential equation. You should also have included the initial condition, y(0) = 4000, since that has to be used to find C.

Okay that was my fault but have you had a go at finding a sloution from the equation stated? Im just curious as I spent alot of time on this question and want to know if correct or not?

Mark44
Mentor
I don't have time right now to check your work, but you can do that. Take your solution y(t) and differentiate it. If you don't get 20sqrt(10)(1 -e^(t/sqrt(10))/(1 + e^(t/sqrt(10)), your solution is incorrect.