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A-rocket-accelerates-straight-up-by-ejecting-gas-downwards-In-a-small-time-interval-t-it-ejects-a-gas-of-mass-m-at-a-relative-speed-u-Calculate-KE-of-the-entire-system-at-t-t-and-t-and-show-th

Question Number 23066 by Tinkutara last updated on 25/Oct/17 $$\mathrm{A}\:\mathrm{rocket}\:\mathrm{accelerates}\:\mathrm{straight}\:\mathrm{up}\:\mathrm{by} \\ $$$$\mathrm{ejecting}\:\mathrm{gas}\:\mathrm{downwards}.\:\mathrm{In}\:\mathrm{a}\:\mathrm{small} \\ $$$$\mathrm{time}\:\mathrm{interval}\:\Delta{t},\:\mathrm{it}\:\mathrm{ejects}\:\mathrm{a}\:\mathrm{gas}\:\mathrm{of}\:\mathrm{mass} \\ $$$$\Delta{m}\:\mathrm{at}\:\mathrm{a}\:\mathrm{relative}\:\mathrm{speed}\:{u}.\:\mathrm{Calculate}\:\mathrm{KE} \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{entire}\:\mathrm{system}\:\mathrm{at}\:{t}\:+\:\Delta{t}\:\mathrm{and}\:{t}\:\mathrm{and} \\ $$$$\mathrm{show}\:\mathrm{that}\:\mathrm{the}\:\mathrm{device}\:\mathrm{that}\:\mathrm{ejects}\:\mathrm{gas} \\ $$$$\mathrm{does}\:\mathrm{work}\:=\:\left(\frac{\mathrm{1}}{\mathrm{2}}\right)\Delta{mu}^{\mathrm{2}} \:\mathrm{in}\:\mathrm{this}\:\mathrm{time} \\ $$$$\mathrm{interval}\:\left(\mathrm{neglect}\:\mathrm{gravity}\right).…

show-that-the-variance-2-of-a-set-of-observations-x-1-x-2-x-n-with-mean-x-can-be-expressed-in-the-form-2-i-1-n-x-i-2-n-x-2-

Question Number 88592 by Rio Michael last updated on 11/Apr/20 $$\mathrm{show}\:\mathrm{that}\:\mathrm{the}\:\mathrm{variance}\:\delta^{\mathrm{2}} \:\mathrm{of}\:\mathrm{a}\:\mathrm{set}\:\mathrm{of}\:\mathrm{observations}\:{x}_{\mathrm{1}} ,{x}_{\mathrm{2}} ,…{x}_{{n}} \:\mathrm{with}\:\mathrm{mean} \\ $$$$\overset{\_} {{x}}\:\mathrm{can}\:\mathrm{be}\:\mathrm{expressed}\:\mathrm{in}\:\mathrm{the}\:\mathrm{form}\:\:\delta^{\mathrm{2}} \:=\:\frac{\underset{{i}=\mathrm{1}} {\overset{{n}} {\sum}}{x}_{{i}} ^{\mathrm{2}} }{{n}}\:−\:\bar {{x}}\:^{\mathrm{2}\:} \\…

A-particle-of-mass-m-strikes-on-ground-with-angle-of-incidence-45-If-coefficient-of-restitution-e-1-2-find-the-velocity-after-impact-and-angle-of-reflection-

Question Number 23049 by Tinkutara last updated on 25/Oct/17 $$\mathrm{A}\:\mathrm{particle}\:\mathrm{of}\:\mathrm{mass}\:{m}\:\mathrm{strikes}\:\mathrm{on}\:\mathrm{ground} \\ $$$$\mathrm{with}\:\mathrm{angle}\:\mathrm{of}\:\mathrm{incidence}\:\mathrm{45}°.\:\mathrm{If}\:\mathrm{coefficient} \\ $$$$\mathrm{of}\:\mathrm{restitution},\:{e}\:=\:\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}}\:,\:\mathrm{find}\:\mathrm{the}\:\mathrm{velocity} \\ $$$$\mathrm{after}\:\mathrm{impact}\:\mathrm{and}\:\mathrm{angle}\:\mathrm{of}\:\mathrm{reflection}. \\ $$ Answered by ajfour last updated on 25/Oct/17…

Question-154100

Question Number 154100 by solihin last updated on 14/Sep/21 Answered by peter frank last updated on 14/Sep/21 $$\sqrt{\mathrm{a}}\:+\sqrt{\mathrm{b}}\:=\sqrt{\mathrm{c}} \\ $$$$\left(\sqrt{\mathrm{a}}\:+\sqrt{\mathrm{b}}\right)^{\mathrm{2}} =\left(\sqrt{\mathrm{c}}\:\right)^{\mathrm{2}} \\ $$$$\mathrm{a}+\mathrm{2}\sqrt{\mathrm{ab}}\:+\mathrm{b}=\mathrm{c} \\ $$$$\mathrm{5x}+\mathrm{1}+\mathrm{2}\sqrt{\left(\mathrm{5x}+\mathrm{1}\right)\left(\mathrm{x}−\mathrm{2}\right)}\:=\mathrm{8x}+\mathrm{1}…

pi-6-3pi-4-tanx-1-tanx-dx-

Question Number 88559 by 675480065 last updated on 11/Apr/20 $$\int_{\frac{−\pi}{\mathrm{6}}} ^{\frac{\mathrm{3}\pi}{\mathrm{4}}} \frac{\sqrt{{tanx}}}{\mathrm{1}+\sqrt{{tanx}}}{dx} \\ $$ Commented by MJS last updated on 11/Apr/20 $$\mathrm{t}=\sqrt{\mathrm{tan}\:{x}}\:\rightarrow\:{dx}=\mathrm{2cos}^{\mathrm{2}} \:{x}\:\sqrt{\mathrm{tan}\:{x}}{dt} \\ $$$$\mathrm{this}\:\mathrm{leads}\:\mathrm{to}…

what-are-the-conditions-necessary-for-a-body-of-mass-mkg-on-an-incline-plane-at-angle-to-the-horizontal-to-remain-at-rest-

Question Number 23022 by NECx last updated on 25/Oct/17 $${what}\:{are}\:{the}\:{conditions}\:{necessary} \\ $$$${for}\:{a}\:{body}\:{of}\:{mass}\:{mkg}\:{on}\:{an}\:{incline}\:{plane} \\ $$$${at}\:{angle}\:\theta\:{to}\:{the}\:{horizontal}\:{to} \\ $$$${remain}\:{at}\:{rest}? \\ $$ Commented by NECx last updated on 25/Oct/17…

H-f-o-of-N-2-O-is-82-kJ-mol-and-bond-energy-for-N-2-N-N-O-O-and-N-O-bonds-are-946-418-498-and-607-kJ-mol-respectively-then-resonance-energy-of-N-2-O-is-

Question Number 22999 by Tinkutara last updated on 24/Oct/17 $$\Delta\mathrm{H}_{\mathrm{f}} ^{\mathrm{o}} \:\mathrm{of}\:\mathrm{N}_{\mathrm{2}} \mathrm{O}\:\mathrm{is}\:\mathrm{82}\:\mathrm{kJ}/\mathrm{mol}\:\mathrm{and}\:\mathrm{bond} \\ $$$$\mathrm{energy}\:\mathrm{for}\:\mathrm{N}_{\mathrm{2}} ,\:\mathrm{N}\:=\:\mathrm{N},\:\mathrm{O}\:=\:\mathrm{O}\:\mathrm{and}\:\mathrm{N}\:=\:\mathrm{O} \\ $$$$\mathrm{bonds}\:\mathrm{are}\:\mathrm{946},\:\mathrm{418},\:\mathrm{498}\:\mathrm{and}\:\mathrm{607}\:\mathrm{kJ}/\mathrm{mol} \\ $$$$\mathrm{respectively},\:\mathrm{then}\:\mathrm{resonance}\:\mathrm{energy}\:\mathrm{of} \\ $$$$\mathrm{N}_{\mathrm{2}} \mathrm{O}\:\mathrm{is} \\ $$…

For-which-of-the-following-the-hydration-energy-of-Mg-2-is-larger-1-Na-2-Al-3-3-Be-2-4-Cr-3-

Question Number 22993 by Tinkutara last updated on 24/Oct/17 $$\mathrm{For}\:\mathrm{which}\:\mathrm{of}\:\mathrm{the}\:\mathrm{following},\:\mathrm{the} \\ $$$$\mathrm{hydration}\:\mathrm{energy}\:\mathrm{of}\:\mathrm{Mg}^{\mathrm{2}+} \:\mathrm{is}\:\mathrm{larger}? \\ $$$$\left(\mathrm{1}\right)\:\mathrm{Na}^{+} \\ $$$$\left(\mathrm{2}\right)\:\mathrm{Al}^{\mathrm{3}+} \\ $$$$\left(\mathrm{3}\right)\:\mathrm{Be}^{\mathrm{2}+} \\ $$$$\left(\mathrm{4}\right)\:\mathrm{Cr}^{\mathrm{3}+} . \\ $$ Answered…