A particle fall from height $h$ on $a$ static horizontal plane rebounds. If $e$ is coefficient of restitution then before coming to rest the total distance travelled during rebounds will be:-
$h\left( {\frac{{1 + {e^2}}}{{1 - {e^2}}}} \right)$
$h\left( {\frac{{1 - {e^2}}}{{1 + {e^2}}}} \right)$
$\frac{h}{2}\left( {\frac{{1 - {e^2}}}{{1 + {e^2}}}} \right)$
$\frac{h}{2}\left( {\frac{{1 + {e^2}}}{{1 - {e^2}}}} \right)$
$A$ man who is running has half the kinetic energy of the boy of half his mass. The man speeds up by $1 \, m/s$ and then has the same kinetic energy as the boy. The original speed of the man was
A particle moves with a velocity $\vec v\, = \,5\hat i - 3\hat j + 6\hat k\,\,m/s$ under the influence of a constant force $\vec F\, = \,10\hat i + 10\hat j + 20\hat k$. Instantaenous power will be ............... $\mathrm{J} / \mathrm{s}$
A particle of mass $m$ strikes the ground inelastically, with coefficient of restitution $e$
Four smooth steel balls of equal mass at rest are free to move along a straight line without friction. The first ball is given a velocity of $0.4\, m/s$. It collides head on with the second elastically, the second one similarly with the third and so on. The velocity of the last ball is .............. $\mathrm{m}/ \mathrm{s}$
When a ball is freely fallen from a given height it bounces to $80\%$ of its original height. What fraction of its mechanical energy is lost in each bounce ?