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Question Number 175010 by Mastermind last updated on 16/Aug/22

$$\mathrm{A}\mathrm{ball}\mathrm{of}\mathbf{p}\mathrm{of}\mathrm{mass}0.25\mathrm{kg}\mathrm{losses}\frac{1}{3}\mathrm{of}$$$$\mathrm{its}\mathrm{velocity}\mathrm{when}\mathrm{it}\mathrm{makes}\mathrm{an}\mathrm{head}\mathrm{on}$$$$\mathrm{collision}\mathrm{with}\mathrm{an}\mathrm{identical}\mathrm{ball}\mathbf{q}\mathrm{at}\mathrm{rest}.$$$$\mathrm{After}\mathrm{collision},\mathbf{q}\mathrm{moves}\mathrm{off}\mathrm{with}\mathrm{a}\mathrm{velocity}$$$$\mathrm{of}{2\mathrm{ms}}^{-1}\mathrm{in}\mathrm{the}\mathrm{original}\mathrm{direction}\mathrm{of}\mathbf{p}.$$$$\mathrm{Calculate}\mathrm{the}\mathrm{initial}\mathrm{velocity}\mathrm{of}\mathbf{p}.$$

Commented by mr W last updated on 16/Aug/22

$$pu=p\frac{2u}{3}+qv$$$$p=q$$$$v=2m/s$$$$\Rightarrow \frac{u}{3}=v$$$$\Rightarrow u=3v=6m/s$$

Answered by MikeH last updated on 16/Aug/22

$$\mathrm{By}\mathrm{PCLM}$$$$0.25\left(u\right)=0.25(u-\frac{u}{3})+0.25\left(2\right)$$$$\Rightarrow 0.25u=0.25\left(\frac{2u}{3}\right)+0.5$$$$\Rightarrow 0.25u=3(0.5)$$$$\Rightarrow u=6\mathrm{m}/\mathrm{s}$$$$\mathrm{initial}\mathrm{speed}\mathrm{of}\mathrm{P}\mathrm{is}6\mathrm{m}/\mathrm{s}$$

Commented by Tawa11 last updated on 16/Aug/22

$$\mathrm{Great}\mathrm{sirs}$$

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