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Category: Vector

A-point-moves-in-x-y-plane-according-to-the-law-x-4-sin-6t-and-y-4-1-cos-6t-Find-distance-traversed-by-the-particle-in-5-seconds-when-x-and-y-are-in-metres-

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Question Number 14939 by Tinkutara last updated on 05/Jun/17 $$\mathrm{A}\:\mathrm{point}\:\mathrm{moves}\:\mathrm{in}\:{x}-{y}\:\mathrm{plane}\:\mathrm{according} \\ $$$$\mathrm{to}\:\mathrm{the}\:\mathrm{law}\:{x}\:=\:\mathrm{4}\:\mathrm{sin}\:\mathrm{6}{t}\:\mathrm{and} \\ $$$${y}\:=\:\mathrm{4}\left(\mathrm{1}\:−\:\mathrm{cos}\:\mathrm{6}{t}\right).\:\mathrm{Find}\:\mathrm{distance}\:\mathrm{traversed} \\ $$$$\mathrm{by}\:\mathrm{the}\:\mathrm{particle}\:\mathrm{in}\:\mathrm{5}\:\mathrm{seconds},\:\mathrm{when}\:{x}\:\mathrm{and} \\ $$$${y}\:\mathrm{are}\:\mathrm{in}\:\mathrm{metres}. \\ $$ Answered by ajfour last updated…

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A-plane-is-inclined-at-an-angle-of-30-with-horizontal-Find-the-component-of-a-force-F-10k-N-perpendicular-to-the-plane-Given-that-z-direction-is-vertically-upwards-

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Question Number 14923 by Tinkutara last updated on 05/Jun/17 $$\mathrm{A}\:\mathrm{plane}\:\mathrm{is}\:\mathrm{inclined}\:\mathrm{at}\:\mathrm{an}\:\mathrm{angle}\:\mathrm{of}\:\mathrm{30}° \\ $$$$\mathrm{with}\:\mathrm{horizontal}.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{component} \\ $$$$\mathrm{of}\:\mathrm{a}\:\mathrm{force}\:\overset{\rightarrow} {{F}}\:=\:−\mathrm{10}\overset{\wedge} {{k}}\mathrm{N}\:\mathrm{perpendicular}\:\mathrm{to} \\ $$$$\mathrm{the}\:\mathrm{plane}.\:\mathrm{Given}\:\mathrm{that}\:{z}-\mathrm{direction}\:\mathrm{is} \\ $$$$\mathrm{vertically}\:\mathrm{upwards}. \\ $$ Answered by ajfour…

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A-car-travelling-at-36-km-h-due-North-turns-West-in-5-seconds-and-maintains-the-same-speed-What-is-the-acceleration-of-the-car-

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Question Number 14921 by Tinkutara last updated on 05/Jun/17 $$\mathrm{A}\:\mathrm{car}\:\mathrm{travelling}\:\mathrm{at}\:\mathrm{36}\:\mathrm{km}/\mathrm{h}\:\mathrm{due}\:\mathrm{North} \\ $$$$\mathrm{turns}\:\mathrm{West}\:\mathrm{in}\:\mathrm{5}\:\mathrm{seconds}\:\mathrm{and}\:\mathrm{maintains} \\ $$$$\mathrm{the}\:\mathrm{same}\:\mathrm{speed}.\:\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{acceleration} \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{car}? \\ $$ Commented by ajfour last updated on 05/Jun/17…

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The-velocity-of-particle-P-due-East-is-4-m-s-and-that-of-Q-is-3-m-s-due-South-What-is-the-velocity-of-P-w-r-t-Q-

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Question Number 14922 by Tinkutara last updated on 05/Jun/17 $$\mathrm{The}\:\mathrm{velocity}\:\mathrm{of}\:\mathrm{particle}\:{P}\:\mathrm{due}\:\mathrm{East}\:\mathrm{is} \\ $$$$\mathrm{4}\:\mathrm{m}/\mathrm{s},\:\mathrm{and}\:\mathrm{that}\:\mathrm{of}\:{Q}\:\mathrm{is}\:\mathrm{3}\:\mathrm{m}/\mathrm{s}\:\mathrm{due} \\ $$$$\mathrm{South}.\:\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{velocity}\:\mathrm{of}\:{P}\:\mathrm{w}.\mathrm{r}.\mathrm{t}. \\ $$$${Q}? \\ $$ Commented by ajfour last updated on 05/Jun/17…

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A-swimmer-crosses-a-flowing-river-of-width-d-to-and-fro-in-time-t-1-The-time-taken-to-cover-the-same-distance-up-and-down-the-stream-is-t-2-If-t-3-is-the-time-the-swimmer-would-take-to-swim-a-dis

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Question Number 14920 by Tinkutara last updated on 05/Jun/17 $$\mathrm{A}\:\mathrm{swimmer}\:\mathrm{crosses}\:\mathrm{a}\:\mathrm{flowing}\:\mathrm{river}\:\mathrm{of} \\ $$$$\mathrm{width}\:{d}\:\mathrm{to}\:\mathrm{and}\:\mathrm{fro}\:\mathrm{in}\:\mathrm{time}\:{t}_{\mathrm{1}} .\:\mathrm{The}\:\mathrm{time} \\ $$$$\mathrm{taken}\:\mathrm{to}\:\mathrm{cover}\:\mathrm{the}\:\mathrm{same}\:\mathrm{distance}\:\mathrm{up} \\ $$$$\mathrm{and}\:\mathrm{down}\:\mathrm{the}\:\mathrm{stream}\:\mathrm{is}\:{t}_{\mathrm{2}} .\:\mathrm{If}\:{t}_{\mathrm{3}} \:\mathrm{is}\:\mathrm{the} \\ $$$$\mathrm{time}\:\mathrm{the}\:\mathrm{swimmer}\:\mathrm{would}\:\mathrm{take}\:\mathrm{to}\:\mathrm{swim} \\ $$$$\mathrm{a}\:\mathrm{distance}\:\mathrm{2}{d}\:\mathrm{in}\:\mathrm{still}\:\mathrm{water},\:\mathrm{then}\:\mathrm{prove} \\ $$$$\mathrm{that}\:{t}_{\mathrm{1}}…

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Two-vectors-a-and-b-are-parallel-and-have-same-magnitude-Then-they-1-have-same-direction-but-they-are-not-equal-2-are-equal-3-are-not-equal-4-may-or-may-not-be-equal-

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Question Number 14882 by Tinkutara last updated on 05/Jun/17 $$\mathrm{Two}\:\mathrm{vectors}\:\overset{\rightarrow} {{a}}\:\mathrm{and}\:\overset{\rightarrow} {{b}}\:\mathrm{are}\:\mathrm{parallel}\:\mathrm{and} \\ $$$$\mathrm{have}\:\mathrm{same}\:\mathrm{magnitude}.\:\mathrm{Then}\:\mathrm{they} \\ $$$$\left(\mathrm{1}\right)\:\mathrm{have}\:\mathrm{same}\:\mathrm{direction},\:\mathrm{but}\:\mathrm{they}\:\mathrm{are} \\ $$$$\mathrm{not}\:\mathrm{equal} \\ $$$$\left(\mathrm{2}\right)\:\mathrm{are}\:\mathrm{equal} \\ $$$$\left(\mathrm{3}\right)\:\mathrm{are}\:\mathrm{not}\:\mathrm{equal} \\ $$$$\left(\mathrm{4}\right)\:\mathrm{may}\:\mathrm{or}\:\mathrm{may}\:\mathrm{not}\:\mathrm{be}\:\mathrm{equal} \\…

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A-room-has-dimensions-3-m-4-m-5-m-A-fly-starting-at-one-corner-ends-up-at-the-diametrically-opposite-corner-If-the-fly-were-to-walks-what-is-the-length-of-the-shortest-path-it-can-take-

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Question Number 14821 by Tinkutara last updated on 04/Jun/17 $$\mathrm{A}\:\mathrm{room}\:\mathrm{has}\:\mathrm{dimensions}\:\mathrm{3}\:\mathrm{m}\:×\:\mathrm{4}\:\mathrm{m}\:×\:\mathrm{5}\:\mathrm{m}. \\ $$$$\mathrm{A}\:\mathrm{fly}\:\mathrm{starting}\:\mathrm{at}\:\mathrm{one}\:\mathrm{corner}\:\mathrm{ends}\:\mathrm{up}\:\mathrm{at} \\ $$$$\mathrm{the}\:\mathrm{diametrically}\:\mathrm{opposite}\:\mathrm{corner}.\:\mathrm{If} \\ $$$$\mathrm{the}\:\mathrm{fly}\:\mathrm{were}\:\mathrm{to}\:\mathrm{walks},\:\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{length} \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{shortest}\:\mathrm{path}\:\mathrm{it}\:\mathrm{can}\:\mathrm{take}? \\ $$ Answered by ajfour last updated…

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