# Integration help please

• Mar 16th 2013, 08:40 AM
JayRan
Can anyone help with this? I cant integrate at all (Worried)

(a)You decide to make a accurate estimation of the height of a bridge by considering air resistance. By doing a little research you discover that, for a stone, the air resistance (R) is proportional to velocity such that R = 0.009V for that type of stone. If the mass of the stone is 0.4 kg and g = 9.8 ms-2, then apply Newton’s second law of motion to prove that: dv/dt = 9.8-0.225v

(b) This is known as a variable-separable differential equation, which can be written as:
$\displaystyle \int$ 1/ 9.8-0.0225v dv = $\displaystyle \int$ dt

By solving these integrals find
(i) t as a function of v, from which find
(ii) v as a function of t, i.e. show that v=436-435e^-0.0225t

(c) Using v=dx/dt find x as a function of t.

(d) If t = 5 seconds, then what is the height of the bridge? Calculate the percentage error using S = Ut + ½ at2 where a = g = 9.8
• Mar 16th 2013, 09:31 AM
HallsofIvy
Re: Integration help please
I presume you mean $\displaystyle \int \frac{1}{9.8- 0.0225v}dv$. Let u= 9.8- 0.0225v.

(What you wrote was $\displaystyle \int (\frac{1}{9.8}- 0.0225v)dv$.)
• Mar 16th 2013, 09:42 AM
JayRan
Re: Integration help please
Yea thats what i meant. Thanks
• Mar 16th 2013, 10:38 AM
JayRan
Re: Integration help please
Solved it. Thanks anyway.