Calculating Particle Collision Time and Speeds in Vertical Projection

[Jess1986]

2 particles are projected vertically up one after another from the same point at same initial speed u. T is the time interval between the 2 projections, where T<2u/g. Find what further time elapses before the particles collide, and find their speeds immediately before impact.

The particles will collide when they are at equal height. I've started by finding the distance formula for particle 1 but am unsure how i should use T in an equation for particle 2??

 

[greytomato]

try drawing a graph of height as a function of time for both particles.
(time is the horizontal axis, height is the vercital axis)
since there are no other forces at play here (besides gravitation) then you can draw the movement of particle1 as a parabula. the same goes for particle2.
after you've done this you should be able to figure out where to go from there.

if you're having trouble understanding me please let me know and i'll try adding a sketch.

 

[Jess1986]

ive made a sketch and it is clear of the point when the particles collide. I have not solved these type of problems using graphs before. How do i go about finding the time of collision?

 

[greytomato]

i believe it's always better to visualize the problem.
the particle movement is identical. everything is the same except for the time of launch.
let's call:
T0 = time of launching particle1.
gap = the gap between the launches.
T1 = time of collision.
so on the equation of particle2 just place (T-gap) instead of T.
**note the negative sign
you should be able to continue from there.

 

[Jess1986]

the equations i have are for the distance traveled by the particles and not the height reached. As the particles will have traveled different distances when they reach the same height this will not work. How do i find equations for height?