Question

you are standing on a 100m tall buiding above a street and your friend is standing vertically below the building. When you drop a stone, your friend simultaneously throws the identical stone as yours at a speed of 50m/s in the same straight line. Calculate the time taken for the stones to collide

Answer 1

Let the heights of the two stones above the ground be Y1 and Y2.

Y1 = 100 - 4.9 t^2 (the dropped stone)
Y2 = -4.9 t^2 + 50 t (the thrown-upward stone)

Now set Y1 = Y2 and solve for t.

The t^2 terms drop out and you get an easy linear equation to solve.
Enjoy!