In addition to that velocity formula, you should also have the height formula, \(\displaystyle h= -(g/2)t^2+ ut\). For the two different stones, label the variable with subscripts 1 and 2: for the first stone \(\displaystyle h_1= -(g/2)t_1^2+ u_1t_1\) and for the second stone \(\displaystyle h_2= -(g/2)t_2^2+ u_2t_1\). The first stone is throw upward with initial speed \(\displaystyle u_1= 25\) so \(\displaystyle h_1= -(g/2)t_1^2+ 25t_1\). The second stone is thrown upward at the same speed so \(\displaystyle h_2= -(g/2)t_2^2+ 25t_2\). Further, the second stone is thrown 4 seconds later so \(\displaystyle t_2= t_1+ 4\).
We have \(\displaystyle h_1= -(g/2)t_1^2+ 25t_1\) and \(\displaystyle h_2= -(g/2)(t_1+ 4)^2+ 25(t_1+ 4)= -(g/2)(t_1^2+ 8t_1+ 16)+ 25t_1+ 100\). They will meet when they have the same height: \(\displaystyle h_1= h_2\) or \(\displaystyle -(g/2)t_1^2+ 25t_1= -(g/2)t_1^2- 4gt_1- 8g+ 25t_1+ 100\). Solve that equation for \(\displaystyle t_1\). when they meet. Put that value for \(\displaystyle t_1\) into the equation for \(\displaystyle h_1\) to determine where they meet.
