Find the time at which the balls cross each other.............?

Question

A stone is dropped from a height 'h'. Simultaneously another stone is thrown the it can reach a height '4h'. the two stones cross each other after time.....????

Answer 1

For the second stone:

Conservation of energy

m*g*4*h=0.5*m*vi^2 so vi=sqr(8*g*h) (1)

x2=vi*t-0.5*g*t^2

For the first stone:

x1=0.5*g*t^2

The two stones cross each other:

x1+x2=h

0.5*g*t^2+vi*t-0.5*g*t^2=h

vi*t=h

t=h/vi and using (1)

t=h/sqr(8*g*h)