A ball is dropped from the roof of a tall building and simultaneously another ball is thrown horizontally with some velocity from the same roof. Which ball lands first ? Explain your answer.

Explanation

Let height of the building = Displacement = h
For first ball u = 0, S = h, a = g, `t=t_(1)`
Substituting these values in `S=ut+1/2at^(2)`
`" "rArr h=0+1/2gt_(1)""^(2)`
`therefore t_(1)=sqrt((2h)/g)" .....(1)"`
For second ball, `u_(x)=u" (say) "u_(x)=0, a_(y)=g, S_(y)=h, t=t_(2)`
Substituting these values in
`S_(y)=u_(y)t+1/2a_(y)t^(2)`
`h=0+1/2gt_(2)""^(2)`
`therefore t_(2)=sqrt((2h)/g)" .....(2)"`
From equation (1) and equation (2), `t_(1)=t_(2)`
`therefore` Two balls will reach the ground in same time.