Three-towns-X-Y-and-Z-are-on-a-straight-road-and-Y-is-the-mid-way-between-X-and-Z-A-motor-cyclist-moving-with-uniform-acceleration-passes-X-Y-and-Z-The-speed-with-which-the-motocyclist-passes-X-a

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Question Number 26328 by tawa tawa last updated on 24/Dec/17

$$\mathrm{Three}\mathrm{towns}\mathrm{X},\mathrm{Y}\mathrm{and}\mathrm{Z}\mathrm{are}\mathrm{on}\mathrm{a}\mathrm{straight}\mathrm{road}\mathrm{and}\mathrm{Y}\mathrm{is}\mathrm{the}\mathrm{mid}-\mathrm{way}\mathrm{between}$$$$\mathrm{X}\mathrm{and}\mathrm{Z}.\mathrm{A}\mathrm{motor}\mathrm{cyclist}\mathrm{moving}\mathrm{with}\mathrm{uniform}\mathrm{acceleration}\mathrm{passes}\mathrm{X},\mathrm{Y}\mathrm{and}\mathrm{Z}.$$$$\mathrm{The}\mathrm{speed}\mathrm{with}\mathrm{which}\mathrm{the}\mathrm{motocyclist}\mathrm{passes}\mathrm{X}\mathrm{and}\mathrm{Z}\mathrm{are}20\mathrm{m}/\mathrm{s}\mathrm{and}40\mathrm{m}/\mathrm{s}$$$$\mathrm{respectively}.\mathrm{Find}\mathrm{the}\mathrm{speed}\mathrm{with}\mathrm{which}\mathrm{the}\mathrm{motorcyclist}\mathrm{passes}\mathrm{Y}.$$

Commented by tawa tawa last updated on 24/Dec/17

$$\mathrm{please}\mathrm{help}.$$

Answered by jota@ last updated on 25/Dec/17

$$$$$$s_Z-s_X=2(s_Y-s_X).$$$$$$$$v_Z^2-v_X^2=2a(s_Z-s_X)$$$$1200=2a(s_Z-s_X)=4a(s_Y-s_X)$$$$600=2a(s_Y-s_X).$$$$v_Y^2=v_X^2+2a(s_Y-s_X)$$$$v_Y^2=400+600$$$$v_Y=10\sqrt{10}$$

Commented by tawa tawa last updated on 25/Dec/17

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

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