question_answer

A body is thrown vertically up from a certain height and another thrown vertically down from the same point with the same speed at the same time. If they hit the ground with a time gap of 4s, find the speed of projection.  \[(g=10\text{ }m{{s}^{-2}})\]

Answer:

Projected vertically upwards: \[h=u{{t}_{1}}-\frac{1}{2}gt_{1}^{2}\]                     ??????..(1) Projected vertically downwards: \[-h=-u{{t}_{2}}-\frac{1}{2}gt_{2}^{2}\] ??????..(2) From (1) & (2) we get, \[{{t}_{1}}-{{t}_{2}}=\frac{2u}{g}\] \[\Rightarrow 4=\frac{2u}{10}\Rightarrow u=\frac{4\times 10}{2}=20m/s\]