https://file.aiquickdraw.com/mathbot/file/1728312551894r2gjueiu.jpg

Let's go through the questions and solve them step by step:

### Question 8:
**Problem:**
The blue marble is moving from left to right at a velocity of 2 m/s. The orange marble is moving in the opposite direction but at an equal speed. What is the velocity of the orange marble before the collision?

**Solution:**
Since the orange marble is moving in the opposite direction with the same speed, we assign a negative sign to its velocity.

\[
\text{Velocity of the orange marble} = -2 \, \text{m/s}
\]

---

### Question 9:
**Problem:**
During the collision, both marbles accelerate to a stop (0 m/s). Use the formula 
\[
\Delta v = v_{\text{final}} - v_{\text{initial}}
\]
to calculate the change in velocity for the marbles.

- **For the orange marble:**

\[
\Delta v_{\text{orange}} = 0 \, \text{m/s} - (-2 \, \text{m/s}) = 2 \, \text{m/s}
\]

- **For the blue marble:**
We are given that its initial velocity is 2 m/s and it stops after the collision.

\[
\Delta v_{\text{blue}} = 0 \, \text{m/s} - 2 \, \text{m/s} = -2 \, \text{m/s}
\]

So the blue marble's change in velocity is \( -2 \, \text{m/s} \).

---

### Question 10:
**Problem:**
What can you say about the change in velocities of the marbles?

**Solution:**
The change in velocity for the orange marble is positive (+2 m/s), indicating it gained velocity in the positive direction (or slowed down from its negative direction to 0). The blue marble, on the other hand, had a negative change in velocity (-2 m/s), indicating it lost velocity in the positive direction (slowed down to 0 from 2 m/s). 

Thus, both marbles experienced a change in velocity of 2 m/s, but in opposite directions: the orange marble's velocity increased by 2 m/s (toward zero from the negative direction), and the blue marble's velocity decreased by 2 m/s.

---

### Question 11:
**Problem:**
The velocities of the marbles change, so we know that the marbles accelerate. Acceleration is the rate of change of velocity, which is the change in velocity divided by time. What can you say about the accelerations of the blue and orange marbles during the collision?

**Solution:**
Since the time of the collision is the same for both marbles and the magnitudes of their changes in velocity are equal (both changed by 2 m/s), the magnitudes of their accelerations will also be the same. 

Thus, both the orange and blue marbles experience equal accelerations in magnitude but in opposite directions. If one is considered positive, the other will be negative.

---

Would you like more details on any part? Here are 5 relative questions to expand on the concepts:

1. What is the formula for acceleration if the time of the collision is known?
2. How would the problem change if the masses of the marbles were given?
3. Can you calculate the impulse on each marble during the collision?
4. What is the significance of a negative velocity in physics?
5. How would the outcome change if the collision were not perfectly elastic?

**Tip:** When dealing with collisions, always pay attention to the direction of velocities. Opposite directions are often handled using positive and negative signs in physics to represent these directions clearly.

Before the collision, the blue marble is moving from left to right, and it has a velocity of 2 m/s. The orange marble is moving at an equal speed but in the opposite direction. What is the velocity of the orange marble before the collision?

Learn how to calculate the velocity change of two marbles during a collision using basic kinematic principles. This problem involves calculating the change in velocity using the formula Δv = v_final - v_initial, considering the motion in opposite directions. Suitable for high school students in Grades 9-11.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation