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Let's solve part (a) and (b) of the problem step-by-step.

### Part (a)
We are asked to calculate the acceleration of the rocket sled when only one rocket is burning. The following information is given:

- Mass of the system (\( m \)) = 2090 kg
- Thrust (\( T \)) = \( 1.3 \times 10^4 \) N
- Force of friction (\( f \)) = 720 N

From Newton's second law, we know that the net force acting on the sled is the thrust force minus the frictional force. This net force is responsible for the sled's acceleration. The equation is:

\[
F_{\text{net}} = T - f
\]

Then, to find the acceleration, we use the formula:

\[
a = \frac{F_{\text{net}}}{m} = \frac{T - f}{m}
\]

Substituting the values:

\[
a = \frac{1.3 \times 10^4 \, \text{N} - 720 \, \text{N}}{2090 \, \text{kg}}
\]

\[
a = \frac{12,280 \, \text{N}}{2090 \, \text{kg}}
\]

\[
a \approx 5.88 \, \text{m/s}^2
\]

So, the acceleration of the rocket sled with only one rocket burning is approximately **5.88 m/s²**.

---

### Part (b)
Now, we are asked why the acceleration is not exactly one-fourth when all rockets are burning, even though the acceleration with all rockets burning is 25 m/s².

If the thrust provided by one rocket gives an acceleration of 5.88 m/s², we might expect that burning all four rockets would result in an acceleration that is four times larger:

\[
a_{\text{expected}} = 4 \times 5.88 \, \text{m/s}^2 = 23.52 \, \text{m/s}^2
\]

However, the actual acceleration when all rockets are burning is given as **25 m/s²**, which is slightly higher than expected. The reason for this difference is that friction remains constant at 720 N, regardless of the number of rockets burning. 

When more rockets are burning, the thrust increases, but friction doesn't scale up with the thrust. As a result, the friction becomes less significant as the total thrust increases, leading to a slightly higher acceleration than a simple linear scaling would suggest.

---

Do you want further details on these calculations, or have any questions? Here are some related questions you might want to explore:

1. How would the acceleration change if the mass of the sled was different?
2. What would the net force be if all four rockets were burning?
3. How does friction affect the motion of objects in real-world applications?
4. Could air resistance also play a role in real rocket sled scenarios?
5. How would you calculate the work done by the frictional force over a certain distance?

**Tip**: Always remember to factor in non-linear relationships when dealing with real-world problems, as certain forces like friction may not scale directly with thrust or speed.

(a) If the rocket sled starts with only one rocket burning, what is the magnitude of its acceleration (in m/s²)? The mass of the system is 2090 kg, the thrust is 1.3 × 10⁴ N, and the force of friction opposing the motion is 720 N. (b) Why is the acceleration not exactly one-fourth of what it is with all rockets burning? The acceleration when all four rockets are burning is 25 m/s². The force of friction remains 720 N.

Learn how to calculate the acceleration of a rocket sled with one rocket burning. The system has a mass of 2090 kg, a thrust of 1.3 × 10⁴ N, and experiences a frictional force of 720 N. Explore the explanation for why acceleration doesn't scale linearly with multiple rockets.

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