A rifle bullet loses $1/20th$ of its velocity in passing through a plank. The least number of such planks required just to stop the bullet is
$5$
$10$
$11$
$20$
A rifle bullet loses $1/20th$ of its velocity in passing through a plank. The least number of such planks required just to stop the bullet is
Let the thickness of one plank is $s$ if bullet enters with velocity $u$ then it leaves with velocity
$v = \left( {u - \frac{u}{{20}}} \right) = \frac{{19}}{{20}}u$ from ${v^2} = {u^2} - 2as$
$⇒$ ${\left( {\frac{{19}}{{20}}u} \right)^2} = {u^2} - 2as$
$⇒$ $\frac{{400}}{{39}} = \frac{{{u^2}}}{{2as}}$
Now if the n planks are arranged just to stop the bullet then again from ${v^2} = {u^2} - 2as$ $0 = {u^2} - 2ans$
$⇒$ $n = \frac{{{u^2}}}{{2as}} = \frac{{400}}{{39}}$
$⇒$ $n = 10.25$ As the planks are more than $10$ so we can consider $n = 11$
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