Hi there!

We can use the conservation of angular momentum to solve. 

Recall the equation for angular momentum:

We can begin by writing out the scenario as a conservation of angular momentum:

 = moment of inertia of the merry-go-round (kgm²)
 = moment of inertia of the merry-go-round (kgm²)
 = angular velocity of merry go round (rad/sec)
 = angular velocity of merry go round (rad/sec)
 = final angular velocity of COMBINED objects (rad/sec)
 = final angular velocity of COMBINED objects (rad/sec)
 = moment of inertia of boy (kgm²)
 = moment of inertia of boy (kgm²)
 = angular velocity of the boy (rad/sec)
= angular velocity of the boy (rad/sec)
The only value not explicitly given is the moment of inertia of the boy. 
Since he stands along the edge of the merry go round:

We are given that he jumps on the merry-go-round at a speed of 5 m/s. Use the following relation:


Plug in the given values:

Now, we must solve for the boy's moment of inertia:

Use the above equation for conservation of momentum:
