This question involves the concepts of the equations of motion, kinetic energy, and potential energy.
a. The kinetic energy of the rocket at launch is "3.6 J".
b. maximum gravitational potential energy of the rocket is "3.6 J".
<h3>a. KINETIC ENERGY AT LAUNCH</h3>
The kinetic energy of the rocket at launch is given by the following formula:

where,
- K.E = initial kinetic energy = ?
- m = mass of rocket = 0.05 kg
= initial speed = 12 m/s
Therefore,

K.E = 3.6 J
<h3>
b. MAXIMUM GRAVITATIONAL POTENTIAL ENERGY</h3>
First, we will use the third equation of motion to find the maximum height reached by rocket:

where,
- g = -9.81 m/s²
- h = maximum height = ?
- vf = final speed = 0 m/s
Therefore,
2(-9.81 m/s²)h = (0 m/s)² - (12 m/s)²
h = 7.34 m
Hence, the maximum gravitational potential energy will be:
P.E = mgh
P.E = (0.05 kg)(9.81 m/s²)(7.34 m)
P.E = 3.6 J
Learn more about the equations of motion here:
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<span>Stainless steel is a metal alloy
that made up mainly of carbon and chromium. In combination
with low carbon contents, chromium is highly reactive element that imparts
remarkable resistance to corrosion and heat.</span>
Moreover, stainless
steel is mixed up with sufficient nickel, which is an essential allying element
in the series of stainless steel grades. Other components are manganese,
molybdenum, silicon, titanium, aluminum, niobium, copper, nitrogen, and sulfur.
<span>In order to determine the speed of the entire assembly, we employ conservation of momentum. Momentum p = mv where m is the object's mass and v is the velocity.
The putty ball's initial momentum p1 = 0.3kg*6m/s = 1.8 kg*m/s
That momentum is conserved, so the momentum of the new system having mass 0.3 kg + 1.2 kg = 1.5 kg is:
1.8 kg*m/s = 1.5kg*v. Solving for v, we find that the velocity is 1.2 meters/second.</span>