A particle is projected vertically from the ground takes time \( t_{1}=1 \mathrm{~s} \) upto poi...

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A particle is projected vertically from the ground takes time \( t_{1}=1 \mathrm{~s} \) upto point \( \mathrm{A}, t_{2}=3 \mathrm{~s} \) from point A to \( B \), and time \( t_{3} \) \( =4 \mathrm{~s} \) from point \( B \) to highest point. Find the height of the middle point of \( A \) and \( B \) from the ground.
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