We know that arc length (x(t)) is given with the following formula:

Where r is the radius of the barrel. We must keep in mind that as barrel rolls its radius decreases because less and less tape is left on it.
If we say that the thickness of the tape is D then with every full circle our radius shrinks by d. We can write this down mathematically:

When we plug this back into the first equation we get:

We must solve this quadratic equation.
The final solution is:

It is rather complicated solution. If we asume that the tape has no thickness we get simply:
 
 
        
        
        
A bowler throws a bowling ball that rolls down the lane, im like 98% sure it’s that one
        
             
        
        
        
Answer:
a)  1321.45 N
b)  1321.45 N
c)  2.66 m/s^2
d) 2.21*10^-22 m/s^2
Explanation:
Hello!
First of all, we need to remember the gravitational law:

Were 
    G = 6.67428*10^-11 N(m/kg)^2
    m1 and m2 are the masses of the objects
    r is the distance between the objects.
In the present case 
m1 = earth's mass =  5.9742*10^24 kg
m2 = 497 kg
r = 1.92 earth radii = 1.92 * (6378140 m) = 1.2246*10^7 m
Replacing all these values on the gravitational law, we get:
F = 1321.45 N
a)  and  b)
Both bodies will feel a force with the same magnitude 1321.45 N but directed in opposite directions.
The acceleration can be calculated dividing the force by the mass of the object
c)
a_satellite = F/m_satellite = ( 1321.45 N)/(497 kg)
a_satellite = 2.66 m/s^2
d)
a_earth = F/earth's mass = (1321.45 N)/( 5.9742*10^24 kg)
a_earth = 2.21*10^-22 m/s^2
 
        
             
        
        
        
Answer:
It helps us to be aware of some things that guide us and laws or theories to help us learn further