Final answer:
The rocket must accelerate at a rate of 4 m/s².
Step-by-step explanation:
To calculate the rate at which the rocket must accelerate, we can use the equation v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time taken.
In this case, the rocket starts from rest (u = 0) and attains a velocity of 800 m/s.
The final velocity is related to the acceleration and time taken by the equation v = u + at.
Rearranging the equation to solve for acceleration, we have a = (v - u) / t.
Since the rocket reaches the velocity of 800 m/s in an altitude of 160 km, we can calculate the time taken by dividing the altitude (converted to meters) by the velocity.
Thus, the time taken is 160,000 m / 800 m/s = 200 seconds.
Plugging in the values into the equation, we have a = (800 m/s - 0) / 200 s = 4 m/s².