Answer:
[tex]a=4.19 m/s^{2}[/tex]
Explanation:
In order to solve this problem, we must first draw a free body diagram of the situation. (See attached picture)
from this diagram, we can do the following sum of forces:
[tex]\sum F=ma[/tex]
where m is the mass of the rocket and a is its acceleration.
[tex]F_{e}-mg=ma[/tex]
where [tex]F_{e}[/tex] is the force of exhaust. We can solve this for the acceleration, so we get:
[tex]a=\frac{F_{e}-mg}{m}[/tex]
we can find the force of exhaust by using the momentum formula:
Ft=mv
so we can solve this for the force:
[tex]F_{e}=\frac{mv}{t}[/tex]
the problem already tells us what m/t is equal to, so we can directly substitute:
[tex]F_{e}=(1.75x10^{4}kg/s)(2.40x10^3m/s)[/tex]
which yields:
[tex]F_{e}=42x10^6 N[/tex]
So we can now substitute:
[tex]a=\frac{42x10^6N-(3x10^6kg)(9.81m/s^{2})}{3x10^6kg}[/tex]
so:
[tex]a=4.19 m/s^{2}[/tex]
