A compact car, with mass 
, is moving at 
 toward the east. Sketch the moving car. a. Find the magnitude and direction of its momentum. Draw an arrow on your sketch showing the momentum. b. A second car, with a mass of 2175 kg, has the same momentum. What is its velocity?

Let's break down the problem and solve each part.

### Given:
- **Car 1:**
  - Mass (\(m_1\)): Not given explicitly
  - Velocity (\(v_1\)): Moving east at a certain speed (not specified)
  - Momentum (\(p_1\)): We need to find this.

- **Car 2:**
  - Mass (\(m_2\)): 2175 kg
  - Momentum (\(p_2\)): Same as \(p_1\)
  - Velocity (\(v_2\)): We need to find this.

### Part a: Finding the Magnitude and Direction of Momentum

The momentum of an object is given by the formula:
\[
p = m \times v
\]
where:
- \(p\) is the momentum,
- \(m\) is the mass,
- \(v\) is the velocity.

For Car 1, its momentum will be:
\[
p_1 = m_1 \times v_1
\]
Since the velocity is toward the east, the momentum will also be in the eastward direction.

### Part b: Finding the Velocity of the Second Car

Given that the momentum of the second car is the same as the first car, we can write:
\[
p_2 = p_1 = m_1 \times v_1
\]

For the second car:
\[
p_2 = m_2 \times v_2
\]
Setting the momenta equal:
\[
m_1 \times v_1 = m_2 \times v_2
\]
Solving for \(v_2\):
\[
v_2 = \frac{m_1 \times v_1}{m_2}
\]
This equation tells us the velocity of the second car, which depends on the ratio of the masses and the velocity of the first car.

### Sketch and Momentum Arrow
For the sketch:
- Draw a car moving towards the right (east).
- Draw an arrow pointing to the right to represent the momentum of Car 1.

Would you like a detailed explanation of the next steps or any clarification? Here are five related questions:

1. How does changing the mass of the car affect its momentum?
2. What would happen to the velocity of the second car if its mass were doubled?
3. How do you calculate the momentum of an object with a given mass and velocity?
4. Can two cars with different masses have the same momentum? How?
5. What is the significance of the direction in momentum calculations?

**Tip:** When comparing momenta of two objects, always consider both the mass and velocity to understand their relationship.

Learn how to calculate momentum and velocity for moving cars in this physics problem. Solve for the momentum and find the velocity of a second car with the same momentum as the first. Suitable for high school students studying Newtonian mechanics.

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