Final answer:
The increase in momentum can be calculated using the formula F=(mv-mu)/t, and the velocity of the rocket after the first stage burn is 1.5 m/s.
Step-by-step explanation:
To calculate the increase in momentum, we can use the formula:
F = (mv - mu) / t
Where:
F is the upward force of the rocket (30MN),
m is the mass of the rocket (3000 tonnes or 3,000,000 kg),
v is the final velocity of the rocket (unknown),
u is the initial velocity of the rocket (0 m/s),
and t is the burn time of the rocket (2.5 minutes or 150 seconds).
Plugging in these values, we can find the increase in momentum. Then, using the equation:
p = mv
We can calculate the velocity of the rocket after the first stage burn.
Let's do the calculations:
F = (mv - mu) / t
30MN = (3,000,000v - 0) / 150
30MN * 150 = 3,000,000v
4,500,000N = 3,000,000v
v = 4,500,000N / 3,000,000
v = 1.5 m/s
Therefore, the velocity of the rocket after the first stage burn is 1.5 m/s.