Meeting at a height :Example problem

A particle is dropped from a height of 100 m and another particle is projected vertically up with velocity 50 m/s from the ground along the same line. Find out the position where two particles will meet?

Let the upward direction is positive. And imagine the particles will meet at a distance y from the ground.

For particle A,

                              Y₀ = +100 m

                        u = 0 m/sec

                        a = -10 m/sec2

We know,

For particle B,

                               Y₀ = 0 m

                        u = +50 m/sec

                        a = -10 m/sec2

Also,

From (1) and (2), by equating, we will get

                        t = 2 sec.

By putting t =2 sec in equation (1) or (2), you will get, y =80 m.

It means, the particle will meet at a height of 80 m from ground.