The Apollo spacecrafts were launched toward the moon using the Saturn rocket, the most powerful rocket available. Each rocket had five engines producing a total of 3.34 x 10 to the 7thX of force to launch the 2.77 x 10 to the 6 kg spacecraft toward the moon. (a) I need to find the average acceleration of the spacecraft. (b) Than calculate the altitiude of the rocket 2.50 minutes after launch-the point when the spacecraft loses its first stage.

a. a=F/m = 3.34*10^7/2.77*10^6 = 12.06 m/s^2.

b. t = 2.5min * 60s/min = 150 s.

h = 0.5a(2t-1)
h = 6.03*(300-1) = 1803 m.

To find the average acceleration of the spacecraft, we can use Newton's second law of motion, which states that force is equal to mass multiplied by acceleration. The force acting on the spacecraft is 3.34 x 10^7 N, and the mass of the spacecraft is 2.77 x 10^6 kg.

(a) Average acceleration = Force / Mass

Substituting the given values:
Average acceleration = (3.34 x 10^7 N) / (2.77 x 10^6 kg)

Calculating this, we get:
Average acceleration ≈ 12.04 m/s²

Therefore, the average acceleration of the spacecraft is approximately 12.04 m/s².

(b) To calculate the altitude of the rocket 2.50 minutes after launch, we need to use the kinematic equation for displacement:

Displacement = Initial velocity * time + (1/2) * acceleration * time²

Since we want to find the altitude, which is the displacement, we need the initial velocity, time, and acceleration. Given that the point of losing the first stage is 2.50 minutes after launch, we can assume that the initial velocity is 0 m/s since the rocket starts from rest at launch and that acceleration remains constant at the average acceleration found in part (a).

Initial velocity (u) = 0 m/s
Time (t) = 2.50 minutes = 150 seconds
Average acceleration (a) = 12.04 m/s²

Substituting these values into the kinematic equation:
Displacement = 0 * 150 + (1/2) * 12.04 * (150^2)

Calculating this, we get:
Displacement ≈ 27,090 meters

Therefore, the altitude of the rocket 2.50 minutes after launch, when it loses its first stage, is approximately 27,090 meters.