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A falling stone takes 0.25 to fall acros...

A falling stone takes 0.25 to fall across a window which is 1 m high. From how far above the top of the window was the stone dropped (take `g=10m//s^(2)`)?

Text Solution

Verified by Experts

Let the particle be dropped from O and it takes t s to fall up to A, so
`OA=ut+(1)/(2)"gt"^(2)=0+(1)/(2)"gt"^(2)" "(because u=0)`
`OA=(1)/(2)"gt"^(2)`
and `OB=(1)/(2)g(t+0.2)^(2)`
Since, `OB-OA=1m`
`(1)/(2)g[(t+0.2)^(2)-t^(2)]=1`
`rArr" "5[t^(2)+0.4t+0.04-t^(2)]=1`
`rArr" "5[0.4t+0.04]=1`
`rArr" "2t+0.2=1`
`rArr" "2t=1-0.2=0.8`
`rArr" "t=(0.8)/(2)=0.4s`
So, `OA=(1)/(2)xx10xx0.4xx0.4=0.8m`
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