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Physics · MOTION IN A STRAIGHT LINE
हिन्दीA body thrown vertically upwards with initial speed \( u \) crosses a point at height \( h \) above the ground at time \( t_1 \) while going up, and again at time \( t_2 \) while coming down. The height \( h \) in terms of \( t_1 \) and \( t_2 \) is:
Correct answer · Option 3
\( \frac{1}{2} g t_1 t_2 \)
Explanation
Equation of motion: \( h = u t - \frac{1}{2}g t^2 \implies \frac{1}{2}g t^2 - u t + h = 0 \). The roots of this quadratic in \( t \) are \( t_1 \) and \( t_2 \). Product of roots \( t_1 t_2 = \frac{h}{\frac{1}{2}g} = \frac{2h}{g} \implies h = \frac{1}{2} g t_1 t_2 \).
