A monkey of mass 20 kg rides on a 40 kg trolley moving with a constant speed of 8 m/s along a horizontal track.If the monkey jumps vertically to grab the overhanging branchof a tree, the speed of the trolley after the monkey has jumped off is :
a)8
b)1
c)4
d)12

Tell us what you think the answer is, and why, and we'll check it for you. But consider this: in order for the trolley to gain or lose speed in the horizontal direction there must be a force acting on it in the horizontal direction.

I think...
momentum of monkey=mom. Of trolley
m1v1=m2v2
(20)(8)=(40)v2 ( speed of trolley would be same as that of trolley)
here v2= 4 m/s...

i think....
momentum of monkey=mom. of trolley


Not necessarily true, although I like that you're thinking about momentum. What is true is that the sum of the momentums of the monkey + trolley is constant. This leads directly to the answer for this problem.