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Category: Mechanics

Question-29924

Question Number 29924 by ajfour last updated on 13/Feb/18 Commented by ajfour last updated on 13/Feb/18 $${On}\:{a}\:{plank}\:{a}\:{small}\:{block}\:{m}\:{is} \\ $$$${kept}.\:{The}\:{plank}\:{is}\:{free}\:{to}\:{rotate} \\ $$$${about}\:{a}\:{horizontal}\:{axis}\:{at}\:{its}\:{end}. \\ $$$${If}\:{released}\:{as}\:{shown},\:{find} \\ $$$${angle},\:{angular}\:{velocity}\:{of}\:{plank}…

Question-29907

Question Number 29907 by ajfour last updated on 13/Feb/18 Commented by ajfour last updated on 13/Feb/18 $${A}\:{boy}\:{swims}\:{at}\:{speed}\:\boldsymbol{{v}}\:{in}\:{still} \\ $$$${water}\:,\:{walks}\:{on}\:{ground}\:{with} \\ $$$${speed}\:\boldsymbol{\mathrm{w}}\:>\:\boldsymbol{{v}}\:.\:\:{If}\:{he}\:{needs}\:{to}\:{cross} \\ $$$${a}\:{river}\:{of}\:{width}\:\boldsymbol{{b}},\:{water}\:{flowing}\: \\ $$$${at}\:{speed}\:\boldsymbol{{u}},\:{find}\:{the}\:{minimum}…

Question-29687

Question Number 29687 by ajfour last updated on 11/Feb/18 Commented by ajfour last updated on 11/Feb/18 $${Find}\:{the}\:{final}\:{velocity}\:{gained}\:{by}\:{a} \\ $$$${tank}\:{of}\:{mass}\:{M},\:{initially}\:{completely} \\ $$$${filled}\:{with}\:{water}\:{and}\:{at}\:{rest},\:{as}\:{it} \\ $$$${slips}\:{on}\:{a}\:{frictionless}\:{ground}\:{owing} \\ $$$${to}\:{a}\:{small}\:{opening}\:{at}\:{its}\:{base}\:{of}…

Question-29611

Question Number 29611 by ajfour last updated on 10/Feb/18 Commented by ajfour last updated on 10/Feb/18 $${Find}\:{direction}\:{cosines}\:{of}\:{vector}\:\bar {\boldsymbol{{r}}}\:. \\ $$$$\left({in}\:{a}\:{cyclic}\:{form}\:{in}\:{terms}\:{of}\right. \\ $$$$\left.\theta,\phi,\:{and}\:\psi\:\right). \\ $$ Commented…