A 1.50 x 103 kg rocket accelerates upwards, from rest with a 1.23 x 10^5N thrust force. Neglecting air resistance, what is the average acceleration of the rocket?

To find the average acceleration of the rocket, we can use Newton's Second Law of Motion, which states:

\[
F_{\text{net}} = m \cdot a
\]

Where:
- \( F_{\text{net}} \) is the net force acting on the rocket (in Newtons, N),
- \( m \) is the mass of the rocket (in kilograms, kg),
- \( a \) is the acceleration (in meters per second squared, m/s²).

### Step 1: Identify the forces acting on the rocket
The two primary forces acting on the rocket are:
1. The **thrust force** (\( F_{\text{thrust}} \)) pushing the rocket upwards.
2. The **gravitational force** (\( F_{\text{gravity}} \)) pulling the rocket downwards.

The gravitational force can be calculated using:

\[
F_{\text{gravity}} = m \cdot g
\]

Where:
- \( g \) is the acceleration due to gravity, approximately \( 9.81 \, \text{m/s}^2 \).

### Step 2: Calculate the gravitational force
Given:
\[
m = 1.50 \times 10^3 \, \text{kg}
\]
\[
g = 9.81 \, \text{m/s}^2
\]

\[
F_{\text{gravity}} = 1.50 \times 10^3 \, \text{kg} \times 9.81 \, \text{m/s}^2 = 1.4715 \times 10^4 \, \text{N}
\]

### Step 3: Calculate the net force acting on the rocket
The net force (\( F_{\text{net}} \)) is the difference between the thrust force and the gravitational force:

\[
F_{\text{net}} = F_{\text{thrust}} - F_{\text{gravity}}
\]

Given:
\[
F_{\text{thrust}} = 1.23 \times 10^5 \, \text{N}
\]

\[
F_{\text{net}} = 1.23 \times 10^5 \, \text{N} - 1.4715 \times 10^4 \, \text{N} = 1.08285 \times 10^5 \, \text{N}
\]

### Step 4: Calculate the average acceleration
Now, using Newton's Second Law:

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

\[
a = \frac{1.08285 \times 10^5 \, \text{N}}{1.50 \times 10^3 \, \text{kg}} = 72.19 \, \text{m/s}^2
\]

### Final Answer:
The average acceleration of the rocket is \( 72.19 \, \text{m/s}^2 \).

Would you like more details or have any questions?

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Here are five related questions:
1. How would air resistance affect the rocket's acceleration?
2. What would happen to the acceleration if the rocket's mass increased?
3. How can we calculate the rocket's velocity after a certain time given this acceleration?
4. What is the significance of thrust force in rocket propulsion?
5. How does gravity vary with altitude and how might that affect this problem?

**Tip:** When calculating net force, always remember to consider all forces acting on the object, including gravity, friction, and air resistance if applicable.

A 1.50 x 10^3 kg rocket accelerates upwards, from rest with a 1.23 x 10^5N thrust force. Neglecting air resistance, what is the average acceleration of the rocket?

Discover how to calculate the average acceleration of a rocket with a mass of 1.50 x 10^3 kg and a thrust force of 1.23 x 10^5 N. This solution uses Newton's Second Law of Motion to consider both thrust and gravitational forces, ideal for high school students in Grades 10-12.

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