The angular momentum is defined as,

Acording to this text we know for conservation of angular momentum that

Where
is initial momentum
is the final momentum
How there is a difference between the stick mass and the bug mass, we define that
Mass of the bug= m
Mass of the stick=10m
At the point 0 we have that,

Where l is the lenght of the stick which is also the perpendicular distance of the bug's velocity
vector from the point of reference (O), and ve is the velocity
At the end with the collition we have

Substituting




Applying conservative energy equation we have


Replacing the values and solving

Substituting
l=\frac{13}{0.54(9.8)}

Answer:
a) 0.31 rad/s
b) 100 J
c) 6.67 W
Explanation:
(a) the force would generate a torque of:

According to Newton 2nd law, the angular acceleration would be

It starts from rest, then after 15s it would achieve a speed of

(b) The distance angle swept by it is:

Hence the work by the child

c) Average power to work per time unit

It has a 10 electrons. Since it's atomic number is 11 it must have 11 protons. Also, given that it has a +1 charge, it has one less electron than protons since they have equal but opposite charges.
The number of protons is the mass number minus the atomic number = 23-11= 12 neutrons.
F=dP/dt. So you want the momentum to change as slowly as possible in time to minimize the force. So as you catch the egg, let your hand move backward with it for awhile, slowly bringing it to a stop. If you hold your hand steady when you catch it the force due to the impact could break it.