Answers:
a) 
b) 
c) 
Explanation:
<h3>a) Impulse delivered to the ball</h3>
According to the Impulse-Momentum theorem we have the following:
(1)
Where:
is the impulse
is the change in momentum
is the final momentum of the ball with mass
and final velocity (to the right) 
is the initial momentum of the ball with initial velocity (to the left) 
So:
(2)
(3)
(4)
(5)
<h3>b) Time </h3>
This time can be calculated by the following equations, taking into account the ball undergoes a maximum compression of approximately
:
(6)
(7)
Where:
is the acceleration
is the length the ball was compressed
is the time
Finding
from (7):
(8)
(9)
(10)
Substituting (10) in (6):
(11)
Finding
:
(12)
<h3>c) Force applied to the ball by the bat </h3>
According to Newton's second law of motion, the force
is proportional to the variation of momentum
in time
:
(13)
(14)
Finally:

If you do this on Earth, then the acceleration of the falling object is 9.8 m/s^2 ... NO MATTER what it's mass is.
If its mass is 10 kg, then the force pulling it down is 98.1 Newtons. Most people call that the object's "weight".
Answer:
The same as the escape velocity of asteorid A (50m/s)
Explanation:
The escape velocity is described as follows:

where
is the universal gravitational constant,
is the mass of the asteroid and
is the radius
and since the scape velocity is 50m/s:

Now, if the astroid B has twice mass and twice the radius, we have that tha mass is: 
and the radius is: 
inserting these values into the formula for escape velocity:

and we have found that
, so the two asteroids have the same escape velocity.
We found that the expression for escape velocity remains the same as for asteroid A, this because both quantities (radius and mass) doubled, so it does not affect the equation.
The answer is
Asteroid B would have an escape velocity the same as the escape velocity of asteroid A