Question

A water rocket has a mass of 0.8kg and is launched in a school playground with an inital upwards force of 12newtons. what is the weight of the rocket in the playground?
What is the inital acceleration of the rocket in the playground?
If this water rocket could were launched from the moon what would be its initial acceleration (rember to find the new weight first)

Answer 1

Weight = (mass) x (gravity).
It always acts downward.

On Earth, the acceleration of gravity is 9.807 m/s².
On the Moon, the acceleration of gravity is 1.623 m/s².

On Earth, the rocket's weight is  (0.8kg) x (9.8 m/s²) = 7.84 newtons

On the Moon, the rocket's weight is  (0.8kg) x (1.62 m/s²) = 1.3 newtons

The force of the rocket engine acts upward.
Its magnitude is 12 newtons. (From the burning chemicals.
Doesn't depend on local gravity. Same force everywhere.)

Now we have all the data we need to mash together and calculate the
answers to the question.  You might choose a different method, but the
machine that I have selected to do the mashing with is Newton's 2nd law
of motion:

                           Net Force = (mass) x (acceleration).
 
Since the question is asking for acceleration, let's first solve Newton's law
for it.  Divide each side by (mass) and we have

                           Acceleration = (net force) / (mass) .

On Earth, the forces on the rocket are

        (weight of 7.84 N down) + (blast of 12 N up) =  4.16 newtons UP (net)

         Acceleration = (4.16 newtons UP) / (0.8 kg) = 5.2 m/s² UP .

On the moon, the forces on the rocket are

         (weight of 1.3 N down) + (blast of 12 N up) = 10.7 newtons UP (net)

         Acceleration = (10.7 newtons UP) / (0.8 kg) = 13.375 m/s² UP