Two-balls-of-mass-500g-and-750g-moving-with-15m-s-and-10m-s-towards-each-other-collides-Find-the-velocities-of-the-ball-after-collision-if-the-coefficient-of-restitution-is-0-8-

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Question Number 22058 by tawa tawa last updated on 10/Oct/17

$$\mathrm{Two}\mathrm{balls}\mathrm{of}\mathrm{mass}500\mathrm{g}\mathrm{and}750\mathrm{g}\mathrm{moving}\mathrm{with}15\mathrm{m}/\mathrm{s}\mathrm{and}$$$$10\mathrm{m}/\mathrm{s}\mathrm{towards}\mathrm{each}\mathrm{other}\mathrm{collides}.\mathrm{Find}\mathrm{the}\mathrm{velocities}\mathrm{of}\mathrm{the}\mathrm{ball}\mathrm{after}$$$$\mathrm{collision},\mathrm{if}\mathrm{the}\mathrm{coefficient}\mathrm{of}\mathrm{restitution}\mathrm{is}0.8$$

Answered by ajfour last updated on 11/Oct/17

$$MV+mv=15m-10M$$$$=15\times 0.5-10\times 0.75=0$$$$\Rightarrow 0.75V+0.5v=0$$$$or3V=-2v\dots \left(i\right)$$$$furthervel.ofsep=e\times vel.ofapp$$$$\Rightarrow V-v=0.8(15+10)=20\dots \left(ii\right)$$$$using\left(i\right)in\left(ii\right):$$$$-\frac{2}{3}v-v=20$$$$\Rightarrow v=-12m/s$$$$V=-\frac{2}{3}v=-\frac{2}{3}\times (-12)=8m/s.$$

Commented by tawa tawa last updated on 11/Oct/17

$$\mathrm{God}\mathrm{bless}\mathrm{you}\mathrm{sir}.$$

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