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### WB JEE 2008

MCQ (Single Correct Answer)

A particle is projected vertically upwards and is at a height h after t1 seconds and again after t2 seconds then

A
$$h = g{t_1}{t_2}$$
B
$$h = {1 \over 2}g{t_1}{t_2}$$
C
$$h = {2 \over g}{t_1}{t_2}$$
D
$$h = \sqrt {g{t_1}{t_2}}$$

## Explanation

Let the initial velocity is u

$$\therefore$$ $$h = ut - {1 \over 2}g{t^2}$$

$$\Rightarrow g{t^2} - 2ut + 2h = 0$$

This is a quadratic in t,

let it has two roots t1 and t2

$$\therefore$$ $${t_1}{t_2} = {{2h} \over g}$$ ( Product of roots )

$$\Rightarrow h = {1 \over 2}g{t_1}{t_2}$$.

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