Answer the following problems. Show your solution. Use GRSA. (5 pts each)
Lesson 1.1
1. What is 80 kg Riana's weight on earth where the acceleration due to gravity is
9.81 m/s2?
2. What is Riana’s weight on the moon where the acceleration due to gravity is
1.62 m/s2?
Lesson 1.2
1. What is the acceleration of a 60 kg object pushed with a force of 1000 N?
2. Find the acceleration of an object with 11 N and 0.9 kg.

Let's solve these problems step by step using the GRSA method (Given, Required, Solution, Answer).

---

### Lesson 1.1

**Problem 1:** What is 80 kg Riana's weight on Earth where the acceleration due to gravity is 9.81 m/s²?

- **Given:**
  - Mass of Riana, \( m = 80 \, \text{kg} \)
  - Acceleration due to gravity on Earth, \( g = 9.81 \, \text{m/s}^2 \)

- **Required:**
  - Weight of Riana on Earth, \( W \) (in Newtons)

- **Solution:**
  - The weight of an object is calculated using the formula:
    \[
    W = m \times g
    \]
    Substituting the given values:
    \[
    W = 80 \, \text{kg} \times 9.81 \, \text{m/s}^2 = 784.8 \, \text{N}
    \]

- **Answer:**
  - Riana's weight on Earth is **784.8 N**.

---

**Problem 2:** What is Riana’s weight on the Moon where the acceleration due to gravity is 1.62 m/s²?

- **Given:**
  - Mass of Riana, \( m = 80 \, \text{kg} \)
  - Acceleration due to gravity on the Moon, \( g_{moon} = 1.62 \, \text{m/s}^2 \)

- **Required:**
  - Weight of Riana on the Moon, \( W_{moon} \) (in Newtons)

- **Solution:**
  - The weight on the Moon is calculated similarly using the formula:
    \[
    W_{moon} = m \times g_{moon}
    \]
    Substituting the given values:
    \[
    W_{moon} = 80 \, \text{kg} \times 1.62 \, \text{m/s}^2 = 129.6 \, \text{N}
    \]

- **Answer:**
  - Riana's weight on the Moon is **129.6 N**.

---

### Lesson 1.2

**Problem 1:** What is the acceleration of a 60 kg object pushed with a force of 1000 N?

- **Given:**
  - Mass of the object, \( m = 60 \, \text{kg} \)
  - Force applied, \( F = 1000 \, \text{N} \)

- **Required:**
  - Acceleration of the object, \( a \) (in m/s²)

- **Solution:**
  - The acceleration can be found using Newton's second law:
    \[
    a = \frac{F}{m}
    \]
    Substituting the given values:
    \[
    a = \frac{1000 \, \text{N}}{60 \, \text{kg}} = 16.67 \, \text{m/s}^2
    \]

- **Answer:**
  - The acceleration of the object is **16.67 m/s²**.

---

**Problem 2:** Find the acceleration of an object with 11 N force and mass 0.9 kg.

- **Given:**
  - Force applied, \( F = 11 \, \text{N} \)
  - Mass of the object, \( m = 0.9 \, \text{kg} \)

- **Required:**
  - Acceleration of the object, \( a \) (in m/s²)

- **Solution:**
  - Using Newton's second law:
    \[
    a = \frac{F}{m}
    \]
    Substituting the given values:
    \[
    a = \frac{11 \, \text{N}}{0.9 \, \text{kg}} \approx 12.22 \, \text{m/s}^2
    \]

- **Answer:**
  - The acceleration of the object is **12.22 m/s²**.

---

Would you like any further details or have any questions?

Here are five related questions you might find interesting:
1. What would Riana's weight be on Jupiter where gravity is 24.79 m/s²?
2. If a 70 kg person stands on a scale in an elevator accelerating upwards at 2 m/s², what would the scale read?
3. How would the acceleration change if the force was doubled for the 60 kg object?
4. Calculate the weight of a 50 kg object on Mars where gravity is 3.71 m/s².
5. What force is required to accelerate a 20 kg object at 5 m/s²?

**Tip:** Always remember that weight depends on the local gravitational field, so it varies between Earth, the Moon, and other celestial bodies.

Explore how to solve physics problems involving weight and acceleration using the GRSA method. Includes detailed solutions for calculating weight on Earth, the Moon, and acceleration with applied forces. Suitable for high school students.

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