Answer:
a) 
b) 
Explanation:
Given the information from the exercise we can calculate the work done by the elevator using the following formula:

a) Considering you and your belongings as a system we know that the elevator is applying a Normal reaction force of:

Since the force applied and the displacement is in the same direction, the work done by the elevator is positive

b) The reaction force applied by the elevator is the same as the weight of the person

Since the force applied and the displacement is in opposite direction, the work done by the elevator is negative

The key to solve this problem is the conservation of momentum. The momentum of an object is defined as the product between the mass and the velocity, and it's usually labelled with the letter
:

The total momentum is the sum of the momentums. The initial situation is the following:

(it's not written explicitly, but I assume that the 5-kg object is still at the beginning).
So, at the beginning, the total momentum is

At the end, we have

(the mass obviously don't change, the new velocity of the 15-kg object is 1, and the velocity of the 5-kg object is unkown)
After the impact, the total momentum is

Since the momentum is preserved, the initial and final momentum must be the same. Set an equation between the initial and final momentum and solve it for
, and you'll have the final velocity of the 5-kg object.
♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️
The force of friction is equal to the product of the vertical force applied by the surface to the object in the coefficient of friction.
♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️
In this question ,
surface vertical force = Weight of the object
Thus ;
svf = ( mass ) × ( gravity acceleration )
_________________________________
If gravity acceleration is 10 :
svf = 10 × 10 = 100 N
So ;
frictional force = 100 × 0.20
frictional force = 20 N
##############################
If gravity acceleration is 9.8 :
svf = 10 × 9.8 = 98 N
So ;
frictional force = 98 × 0.20
frictional force = 19.6 N
_________________________________
♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️
If an object is not at Absolute Zero, then it is
absorbing and radiating thermal (heat) energy.
Because they are placed in different habitable zones