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

To find the height of point B from the ground, we can follow these steps:

### Step 1: Understand the motion of the particle
The particle is projected vertically upwards from point A. It takes time \( t_1 \) to reach point B and then takes an additional time \( t_2 \) to return to the ground from point B.

### Step 2: Use the equations of motion
The total time taken from the point of projection to the point of return to the ground is \( t_1 + t_2 \). We can apply the equations of motion to find the initial velocity \( u \) of the particle.

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