Tuesday

September 2, 2014

September 2, 2014

Posted by **Erica** on Thursday, January 24, 2013 at 12:58am.

m*dv/dt=mg-kv^2

where m is the mass of the skydiver, g is the gravitational constant, and k is the drag coefficient determined by the position of the driver during the dive.

(a)Find the general solution of the differential equation.

(b) Calculate the limit of v(t) as t -> INF.

I just started with dv/dt=g-(k/m)v^2 I dont really know where to go from there. Tried integrating dv/(g-(k/m)v^2) but I get stucked.

The answer for (a) is supposed to be v(t) = sqrt(m/(kv)*(Ce^(2*sqrt(kg/m)*t)-1)/(Ce^(2*sqrt(kg/m)*t)+1)

and for (b)sqrt (mg/k)

- Differential Equations -
**Steve**, Thursday, January 24, 2013 at 11:10amyou have dv/dt = F(v)

use separation of variables to get

v'/F(v) = 1

or

dv/F(v) = dx

Now, F(v) = g-(k/m)v^2 = k/m (a^2-v^2)

where a^2 = gm/k

That integrate into 1/a arctanh(v/a) = t

which is just a big exponential expression like what you show.

arctanh(z) = 1/2 ln((1+z)/(1-z))

The details get messy. If you go to

http://wood.mendelu.cz/math/maw-html/index.php?lang=en&form=ode

you can enter the equation (sorry, no letter constants, but you can use y'=1-2*y**2 to see the method). It will show you t as a function of v, with logs as above. Convert to v as a function of t to encounter the exponentials you want.

**Answer this Question**

**Related Questions**

physics - A falling skydiver has a mass of 123 kg. (a) What is the magnitude of ...

Physics - 1An object is thrown upward at an initial velocity and caught at the ...

physics - a 150 lb skydiver is falling in a head first position at a terminal (...

science - a skydiver experiences a downwar force due to gravity of 700 N and an ...

physics - A skydiver weighs 166 lb. When the skydiver reaches terminal speed, ...

calculus-differential equation - Consider the differential equation: (du/dt)=-u^...

Physical science. - A skydiver who jumps out of a plane that has a forward ...

physics - A skydiver, who weighs 650 N, is falling at a constant speed with his ...

Physics - A skydiver, who weighs 650 N, is falling at a constant speed with his ...

ipc - A skydiver jumps out of a hovering helicopter, so there is no forward ...