A man of mass `m` is moving with a constant acceleration a w.r.t plank is .The plank less on a smooth horizontal floor If the mass of plank `m` then calculate the acceleration of plank and man w.r.t ground and frictional force extended by plank on man

Explanation

FBD of plank:

(only horzontal froces are shown) ` :. a_(1) = (f)/(m)` (i) (acceleration of plank w.r.t. ground)
For man w.r.t plank.
`ma_(1) + f = ma`
From (i) `2ma_(1) = ma rArr a_(1) = a//2`
Acceleration of man w.r.t ground
`bar a_(m) = bar a_(m,p) + bar a_(p) = a +(-(a)/(2)) = (a)/(2)`
`f = (ma)/(2)`