A man of mass 50 kg is standing on one end of a stationary wooden plank resting on a frictionless surface. The mass of the plank is 100 kg its length is 75 m and the coefficient of friction between the man the plank is `0.2` Find the least possible time (in sec) in which the man reach the other end starting from rest and stopping at the other end.

Answer

`10`

Explanation

`a_(1) and a_(2)` w.r.t. ground

`a_(1)=(mumg)/m=2m//s^(2)`
`a_(2)=(mumg)M=1m//s^(2)`
Plank as frame of reference Plank comes to rest
`tanalpha =3=h/t`
`h=3t`
for minimum time, man will acceleration and retard with `a_(1//2)` for equal time interval t Area of v vs t graph = displacement
`1/2(2t)(3t)=75`
`t=5`
minimum time `=2t=10 sec`