A particle is projected vertically from a point A on ground. It takes time $t_1$ to reach point B but still continous to move up. It takes further $t_2$ time to reach the ground from point B. Height of point B from the ground is

Question

$$(a)\;\frac{1}{2} g(t_1+t_2)^2\quad (b)\;g t_1t_2 \quad (c)\;\frac{1}{8} g(t_1+t_2)^2 \quad (d)\frac{1}{2} g t_1t_2$$