A particle is projected vertically upwards from a point A on the ground. It takes `t_(1)` time to reach a point B but it still continues to move up. If it takes further `t_(2)` time to reach the ground from point B then height of point B from the ground is :-

Options

A. ` (1)/(2) g( t_1+t_2)^(2)`
B. ` g t_1 t_2`
C. ` (1)/( 8) g(t_1t_2) ^(2) `
D. ` (1)/(2) gt_1t_2`

Explanation

For complete motion :
` 0= u(t_1+t_2) -(g)/(2) (t_1 +t_2) ^(2) " "rArr " " u=(g(t_1+t_2))/(2) `
From A to B :
AB ` =ut_1+(1)/(2) ( - g) t_1^(2) A rArr " "AB =(g)/(2) (t_1^(2) +t_1t_2) -(gt_1^(2))/(2) =(gt_1t_2)/(2) `
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