Question

A person of mass m is standing on a stationary trolley of mass M on smooth horizontal surface. the distance between the front end of the trolley and point A is d. the horizontal speed with which the person should jump off the trolley such that its front and just passes through point A in time t

Answer 1

mass= m
mass of trolley = M
so, mu1 + Mu2 = mv1 + Mv2

u1= 0
so, 0= mv1 + Mv2
v1 = Mv2/ m

speed= distance/time
v2 = d/t

putting the value in above equation we get 
v1= Md/mt

so option d will be correct 

Answer 2

Explanation:

mass= m

mass of trolley = M

so, mu1 + Mu2 = mv1 + Mv2

u1= 0

so, 0= mv1 + Mv2

v1 = Mv2/ m

speed= distance/time

v2 = d/t

putting the value in above equation we get

v1= Md/mt

so option d will be correct