Answer:
the two ice skater have the same momentum but the are in different directions.
Paula will have a greater speed than Ricardo after the push-off.
Explanation:
Given that:
Two ice skaters, Paula and Ricardo, initially at rest, push off from each other. Ricardo weighs more than Paula.
A. Which skater, if either, has the greater momentum after the push-off? Explain.
The law of conservation of can be applied here in order to determine the skater that possess a greater momentum after the push -off
The law of conservation of momentum states that the total momentum of two or more objects acting upon one another will not change, provided there are no external forces acting on them.
So if two objects in motion collide, their total momentum before the collision will be the same as the total momentum after the collision.
Momentum is the product of mass and velocity.
SO, from the information given:
Let represent the mass of Paula with 
and its initial velocity with 
Let represent the mass of Ricardo with 
and its initial velocity with 
At rest ;
their velocities will be zero, i.e
= = 0
The initial momentum for this process can be represented as :
+ = 0
after push off from each other then their final velocity will be 
and 
The we can say their final momentum is:
+ = 0
Using the law of conservation of momentum as states earlier.
Initial momentum = final momentum = 0
+ = +
Since the initial velocities are stating at rest then ; u = 0
(0) + (0) = +
+ = 0
= -
Hence, we can conclude that the two ice skater have the same momentum but the are in different directions.
B. Which skater, if either, has the greater speed after the push-off? Explain.
Given that Ricardo weighs more than Paula
So 
;
Then 
The magnitude of their momentum which is a product of mass and velocity can now be expressed as:
=
The ratio is
Therefore, Paula will have a greater speed than Ricardo after the push-off.
, while for air it is 
.
