Questions: A Saturn V's mass at liftoff was 2.80 × 10^6 kg, its fuel-burn rate was 1.40 × 10^4 kg / s, and the exhaust velocity was 2.40 × 10^3 m / s. Calculate its initial acceleration.

Solution Steps

To find the initial acceleration of the Saturn V rocket, we can use the rocket thrust equation, which is derived from Newton's second law and the conservation of momentum. The thrust \( F \) produced by the rocket is given by:

\[ F = \dot{m} v_e \]

where:

• \( \dot{m} \) is the fuel-burn rate (\(1.40 \times 10^{4} \, \text{kg/s}\)),
• \( v_e \) is the exhaust velocity (\(2.40 \times 10^{3} \, \text{m/s}\)).

Substitute the given values into the thrust equation:

\[ F = (1.40 \times 10^{4} \, \text{kg/s}) \times (2.40 \times 10^{3} \, \text{m/s}) \]

Calculate the thrust:

\[ F = 3.36 \times 10^{7} \, \text{N} \]

The initial acceleration \( a \) of the rocket can be found using Newton's second law:

\[ F = m a \]

Rearrange to solve for \( a \):

\[ a = \frac{F}{m} \]

Substitute the values for \( F \) and the initial mass \( m = 2.80 \times 10^{6} \, \text{kg} \):

\[ a = \frac{3.36 \times 10^{7} \, \text{N}}{2.80 \times 10^{6} \, \text{kg}} \]

Calculate the initial acceleration:

\[ a = 12.00 \, \text{m/s}^2 \]

Final Answer