If a body looses half of its velocity on penetrating $3 \,cm$ in a wooden block, then how much will it penetrate more before coming to rest ........... $cm$
If a body looses half of its velocity on penetrating $3 \,cm$ in a wooden block, then how much will it penetrate more before coming to rest ........... $cm$
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If a body looses half of its velocity on penetrating $3 \,cm$ in a wooden block, then how much will it penetrate more before coming to rest ........... $cm$
For first condition Initial velocity $= u$, Final velocity $= u/2, s = 3 \,cm $ From ${v^2} = {u^2} - 2as$
==> ${\left( {\frac{u}{2}} \right)^2} = {u^2} - 2as$
==> $a = \frac{{3{u^2}}}{{8s}}$
Second condition Initial velocity$ = u/2$, Final velocity $= 0$ From ${v^2} = {u^2} - 2ax$
==>$0 = \frac{{{u^2}}}{4} - 2ax$
$x = \frac{{{u^2}}}{{4 \times 2a}} = \frac{{{u^2} \times 8s}}{{4 \times 2 \times 3{u^2}}} = s/3 = 1\,cm$
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