Answer:
The speed of the package of mass m right before the collision 
Their common speed after the collision 
Height achieved by the package of mass m when it rebounds 
Explanation:
Have a look to the diagrams attached below.
a.To find the speed of the package of mass m right before collision we have to use law of conservation of energy.
where 
is Kinetic energy and 
is Potential energy.
and 
Considering the fact 
we will plug out he values of the given terms.
So 
Keypoints:
- Sum of energies and momentum are conserved in all collisions.
- Sum of KE and PE is also known as Mechanical energy.
- Only KE is conserved for elastic collision.
- for elastic collison we have
that is co-efficient of restitution.
<u>KE = Kinetic Energy and PE = Potential Energy</u>
b.Now when the package stick together there momentum is conserved.
Using law of conservation of momentum.
where 
.
Plugging the values we have
Cancelling m from both sides and dividing 3 on both sides.
Law of conservation of energy will be followed over here.
c.Now the collision is perfectly elastic
We have to find the value of 
for m mass.
As here 
we can use that if both are moving in right ward with 
then there is a 
velocity when they have to move leftward.
The best option is to use the formulas given in third slide to calculate final velocity of object 
.
So
Now using law of conservation of energy.
The linear momentum is conserved before and after this perfectly elastic collision.
So for part a we have the speed 
for part b we have their common speed 
and for part c we have the rebound height 
.
