Answer: 0.2m
Explanation: Firstly only the Rocket's Weight Compress the spring which can be found by

According to Hooks Law

The part b and c of this question is done in the attachment
Answer:
3.675 m
Explanation:

X-direction | Y-direction
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Hope it helps
To solve this problem we will apply the given concept for torque which explains the relationship between the force applied and the distance to a given point. Mathematically this relationship is given as

Where,
Torque
F = Force
d = Distance
Our values are given as,

Therefore replacing we have that the force is

F = 12.72N
Therefore the least amount of force that you must exert is 12.72N
Base on my research is that in order to balance an equation, you need to make sure that both the reactant and the product of the equation is equal. So base on the problem the product has dihydrogen monoxide. So to make sure this equation to be in balanced you need to add coefficients 2 to the oxygen to make it dioxygen on the left side. The balanced equation is now CH4 + 2O2 = CO2 + 2H2O