Final answer:
The astronaut experiences an apparent weight of 1443 N during launch, which translates to an acceleration of 14.92 m/s². After accounting for Earth's gravity, the actual acceleration of the astronaut due to the rocket's thrusters is 5.12 m/s².
Step-by-step explanation:
To calculate the acceleration of the astronaut in the rocket, we can use Newton's second law of motion, which states that the force acting upon an object is equal to the mass of the object multiplied by its acceleration (F = ma). Given that the apparent weight of the astronaut is the force being experienced (acting as the net force in this case), and knowing the astronaut's actual mass, we can rearrange the equation to solve for acceleration (a = F/m).
The apparent weight of the astronaut is 1443 N, and the mass is 96.7 kg. The acceleration can be calculated as:
a = F/m
a = 1443 N / 96.7 kg
a = 14.92 m/s²
Note that this acceleration includes the acceleration due to gravity (g = 9.8 m/s²), since the apparent weight is higher than what would be if the astronaut was simply stationary on Earth. To find the actual acceleration of the astronaut above gravity, we would subtract Earth's gravitational acceleration:
Actual acceleration = 14.92 m/s² - 9.8 m/s²
Actual acceleration = 5.12 m/s²
This value represents the additional acceleration being experienced by the astronaut due to the rocket's engines, over and above the acceleration due to gravity.