What is the maximum angle to the horizontal at which a stone can be thrown and always be moving away from the thrower ?

Options

A. `sin^(-1)((sqrt(2))/(3))`
B. `sin^(-1)((2sqrt(2))/(3))`
C. `sin^(-1)((1)/(sqrt(3)))`
D. `sin^(-1)(sqrt((2)/(3)))`

Answer

B

Explanation

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))`