A man of mass `m` walks from end `A` to the other end `B` of a boat of mass `M` and length `l.` The coefficient of friction between the man and the boat is `mu` an neglect any resistive force between the boat and the water.

Options

A. If the man runs at his maximum acceleration, the acceleration of the boat is `(m//M)mug`.
B. The minimum time take by the man to reach the other end of the boat is `sqrt((2MI)/((M+m)mug))`
C. If man runs at his maximum acceleration the acceleration of boat is `m/(m+M)mug`
D. The minimum time take by the man to reach the other end of the boat is `sqrt((2ml)/((M+m)mug))`

Answer

A, B

Explanation

Maximum acceleration of the man `=mumg//m=mug`
Maximum acceleration of the boat `=mumg//M`
Maximum relative acceleration
`a_("rel")=mug+mugm/M((M+m))/Mmug`
`S_("rel")=1/2a_("rel")t^2impliest=sqrt((2lM)/(mug(M+m)))`