Help with proof.

[scguy]

If a particle is fired up with a velocity ''u'' then ''t'' seconds later a second particle is fired up with the same initial velocity and from the same place, prove that the particles will meet after:

 

(0.5t+ u/g)

 

Where g is gravity.

 

The equations used are just the basic equations of motion, i have gotten an answer similiar but i cant see how to prove this exactly.

[Primarygun]

You Got (u/g+t)?

[rajama]

Their positions must coincide at time t2, so using x = vt + 0.5at^2:

p1 will move to x = ut2-0.5gt2^2

& p2 will move to x = u(t2-t)-0.5g(t2-t)^2 = ut2 - ut - 0.5g(t2^2 + t^2 - 2tt2)

equating these and canceling terms:

0 = u/g + 0.5t - t2

or t2 = 0.5t + u/g