question_answer

A dust packet is dropped from 9th storey of a multi-storeyed building. In the first second of its free fall another dust packet is dropped from\[{{\text{7}}^{\text{th}}}\] storey 15m below the 9th storey. If both packets reach the ground at same time, then find height of building.

Answer:

From the relation\[h=\frac{1}{2}g{{t}^{2}}\]                                        ?..(i) \[h-15=\frac{1}{2}g{{(t-1)}^{2}}\]                                                              ????(ii) \[\frac{1}{2}g{{t}^{2}}-15=\frac{1}{2}g{{(t-1)}^{2}}\]        [from Eq. (i)]      \[\frac{1}{2}g\left[ {{t}^{2}}-{{(t-1)}^{2}} \right]=15\] \[(t+t-1)(t-t+1)=\frac{15\times 2}{g}=\frac{15\times 2}{10}=3\] \[2t-1=3\] \[\Rightarrow \] \[t=2s\] \[\therefore \] \[h=\frac{1}{2}g{{t}^{2}}=\frac{1}{2}\times 100\times 2\times 2=20\,m\]