# Sketch the velocity-time graph for two particles colliding in vertical motion?

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Two points A and B are located on a vertical line with point A vertically above point B. A particle is released from rest at A and at the same time another particle is projected vertically upwards from B at velocity #v# . The particles collide when the top one has fallen a distance #y# .

The height of point A above point B is #h# .

If #h=100m# , #v=20 ms^-1# and #g=10 ms^-2# , sketch the velocity-time graph, and mark on the graph the #(t,v)# values where the particles collide. Take #v# to be positive upwards.

An earlier part of the question also had you showing that the time to collision was #t=h/v#

Two points A and B are located on a vertical line with point A vertically above point B. A particle is released from rest at A and at the same time another particle is projected vertically upwards from B at velocity

The height of point A above point B is

If

An earlier part of the question also had you showing that the time to collision was

##### 1 Answer

Let,after time

So,for the one,coming down in that time if comes down by distance

so, for the one going up,we can write,

or,

so,

Now,equation of velocity time relationship for the particle going up is

and, for the one going down is

So,when both will meet,the velocity of th one going down will be

Now,these things are plotted to make a graph

Sorry for the drawing got excessively enlarged,but I have tried to mark velocities of the two particles for important time values.

Note, at