A ball of mass m is thrown upward with a velocity `upsilon`. If air exerts an average resisting force F, the velocity with which the ball returns to the thrower is

Options

A. ` vsqrt((overset-w)/(overset-W+F) )`
B. ` vsqrt((overset-W)/(overet-w-F) ) `
C. ` vsqrt((overset-W-F)/(oversetW+F) ) `
D. ` v sqrt(( overset-W+F)/(overset-W)) `

Answer

C

Explanation

For upward motion, net downward acc `(W+F)/(m) , ` m is mass .Let h= height gained
`rArr " "0 =v^(2) -2((overset-W+F)/(m)) h rArr h= ( mv^(2))/(2(overset-W+F))`
For downward motion, net downward acc = ` (overset -W-F)/(m) .Let V' ` = final velocity and displacement =-h
` rArr " "V^(.2) =0^(2) -2 {(overset-W-F)/(m)} {(-mv^(2))/(2(overset-W+F))}rArr V'=Vsqrt((overset-W-F)/(overset-W+F)) `