To develop this problem it is necessary to apply the concepts related to Gravitational Potential Energy.
Gravitational potential energy can be defined as

As M=m, then

Where,
m = Mass
G =Gravitational Universal Constant
R = Distance /Radius
PART A) As half its initial value is u'=2u, then



Therefore replacing we have that,

Re-arrange to find v,



Therefore the velocity when the separation has decreased to one-half its initial value is 816m/s
PART B) With a final separation distance of 2r, we have that

Therefore




Therefore the velocity when they are about to collide is 
The kinetic energy would be 53,775J:)
The formula for force exerted on/by a spring is
F = k*e where k is the spring constant and x is the distance stretched from
unstrained position. This should allow you to find what you need.
Using F = k x e,
where k is the spring constant,
and e is the extension,
The F is her weight = 45 X 0.80
= 36 N
If it is completely elastic, you can calculate the velocity of the second ball from the kinetic energy
<span>v1 = velocity of #1 </span>
<span>v1' = velocity of #1 after collision </span>
<span>v2' = velocity of #2 after collision. </span>
<span>kinetic energy: v1^2 = v1' ^2 + v2' ^2 (1/2 and m cancel out) </span>
<span>5^2 = 4.35^2 + v2' ^2 </span>
<span>v2 = 2.46 m/s <--- ANSWER</span>
That ratio is 2 .
<h3>What is ratio?</h3>
A ratio is the comparison of the two numbers bydivision.
Taking the first two outputs, or the -1/8 and -1/4, we can divide not the second one by the first one to find the
ratio:
-1/4-1/8
When dividing fractions, we multiply by the reciprocal:
-1/4x-8/1
To multiply fractions, multiply straight across:
(-1x-8)/(4x1) 8/4=2
To know more about ratio click-
brainly.com/question/25927869
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