# A ball of mass m is projected vertically up from a smooth horizontal floor with a speed V. Find the total momentum delivered by the ball to the surface during the impact, assuming e as coeff. of restitution.

$Foranobjectbouncingoffastationaryobject,suchasafloor,coefficientofrestitution,e=\sqrt{\frac{h\text{'}}{h}}\phantom{\rule{0ex}{0ex}}h=\frac{{v}^{2}}{2g}visthevelocityatwhichtheballstrikethefloor\phantom{\rule{0ex}{0ex}}thevelocityoftheballafterstrikebev\text{'}upward\phantom{\rule{0ex}{0ex}}h\text{'}=\frac{v{\text{'}}^{2}}{2g},e=\sqrt{\frac{\frac{v{\text{'}}^{2}}{2g}}{\frac{{v}^{2}}{2g}}}\phantom{\rule{0ex}{0ex}}e=\left(\frac{v\text{'}}{v}\right)\phantom{\rule{0ex}{0ex}}v\text{'}=ev\phantom{\rule{0ex}{0ex}}momentumdeliveredisvahngeinmomentum=\left(ev+v\right)m=mv\left(e+1\right)\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}Regards\phantom{\rule{0ex}{0ex}}$

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