Two identical 100 kg objects (of negligible size) are in space 100 m away from each other. The force of gravity causes both objects to accelerate towards one another. Find the time it takes for the objects to collide.

Question

kc_kennylau · Answer

$$\Large f=ma$$$$\Large s=ut+\frac12at^2$$s=50, u=0, f=9.8, m=100

btaylor · Answer

I know that the acceleration (in terms of r) is: $$a(r)=G \frac{100}{r^2}$$where r is the distance between the objects.

I can find the velocity in terms of r by integrating that; I get: $$v(r)=\frac{-300G}{r^3}+C$$
Where do I go from here?

btaylor · Answer

@kc_kennylau the problem deals with non-constant acceleration, so the second equation doesn't work.

kc_kennylau · Answer

lolz ok I don't know how to do xP I'm only in Grade 9 xP

btaylor · Answer

thanks for trying.

kc_kennylau · Answer

no problem

btaylor · Answer

oops...
$$v(r)=-\frac{100G}{r}+C$$

superdavesuper · Answer

Sorry too lazy to write out the equation but here u go:

using r as the distance, acceleration = d2r/dt2
so u have d2r/dt2 = Gx100/r^2
solve the differential equation with the boundary conditions r=0, t=0 and r=50 and t=x where x is ur solution.

btaylor · Answer

Thanks for the reply. How do you use differential equations on the second derivative?

superdavesuper · Answer

Try this: http://en.wikipedia.org/wiki/Classical_central-force_problem#One-dimensional_problem It really more of a physics question than math prob.