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The maximum angle to the horizontal at which a stone can be thrown so that it always moves away from the thrower will be :A. `sin^(-1)((sqrt(2))/(3))`B. `sin^(-1)((2sqrt(2))/(3))`C. `sin^(-1)((1)/(sqrt(3)))`D. `sin^(-1)(sqrt((2)/(3)))` |
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Answer» Correct Answer - B If stone always moves away from thrower then `rArr(d|vecr|)/(dt)gt0` `rArr(d|vecr|)/(dt)gt0` `rArrvecr.vecv gt 0 vecr=u costhetatveci+(u sinthetat-(1)/(2)g t^(2))hatj` `vecv=ucosthetahati+(usintheta-g t)hatj` `vecr.vecv=u^(2)t-(3)/(2)ug sin theta t^(2)+(g^(2))/(2)t^(3)gt0` `rArr (g^(2))/(2) t^(2)-(3)/(2) ug sintheta t+u^(2)gt0` `sin^(2)thetalt(8)/(9)rArrthetaltsin^(-1)((2sqrt(2))/(3))` |
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