A rocket blasts off from rest and attains a speed of 30.4 m/s in 10.3 s. An astronaut has a mass of 60.1 kg. What is the astronaut's apparent weight during takeoff?

To determine the astronaut's apparent weight during takeoff, we need to consider the principles of Newton's second law of motion.

Apparent weight refers to the force experienced by an object due to its contact with a supporting surface. In this case, the supporting surface is the floor of the rocket.

The weight of an object is determined by the force of gravity acting on it, which is given by the formula W = mg, where W is the weight, m is the mass of the object, and g is the acceleration due to gravity (approximately 9.8 m/s² on Earth).

During takeoff, there are two forces acting on the astronaut: their weight force and the force exerted by the accelerating rocket. The net force exerted on the astronaut can be calculated using Newton's second law of motion:

F = ma

Where F is the net force, m is the mass of the astronaut, and a is the acceleration of the astronaut.

To find the net force, we need to know the acceleration of the astronaut. We can calculate this using the formula for acceleration:

a = (v - u) / t

Where v is the final velocity, u is the initial velocity, and t is the time taken.

Given:
Initial velocity (u) = 0 m/s (since the astronaut starts from rest)
Final velocity (v) = 30.4 m/s
Time taken (t) = 10.3 s
Mass of the astronaut (m) = 60.1 kg

Let's calculate the acceleration first:

a = (v - u) / t
= (30.4 - 0) / 10.3
= 2.96 m/s² (approx)

Now, we can calculate the net force:

F = ma
= 60.1 kg * 2.96 m/s²
= 178.556 N (approx)

Therefore, the astronaut's apparent weight during takeoff is approximately 178.556 N.