question_answer

A stone is dropped from the top of tall tower and after one second another stone is dropped from a balcony 20m below the top of the tower. If both the stones reach the ground at the same time. What is the height of the tower? [\[\text{g}=\text{1}0\text{m}{{\text{s}}^{-\text{2}}}\]]

Answer:

\[h=\frac{1}{2}g{{t}^{2}}\]                           ??????..(1) \[h-20=\frac{1}{2}g{{(t-1)}^{2}}\]              ??????..(2) Subtracting (1) and (2) \[\Rightarrow 20=\frac{1}{2}g\left\{ {{t}^{2}}{{(t-1)}^{2}} \right\}\] \[20=5(2t-1)\,\,or\,\,t=2.5\] \[\therefore \,\,h=\frac{1}{2}\times 10\times 6.25=31.25\,\,m\]