https://file.aiquickdraw.com/mathbot/file/17303872198929734flla.jpg

Let’s go through each question step-by-step.

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### Question 4
- **Given:**
  - Mass of ball (\( m \)) = 0.412 kg
  - Initial velocity (\( v \)) = 13.4 m/s
  - Angle of launch = 42.3°
  - Time of collision with post = 0.56 seconds

- **Solution:**
  1. Calculate the momentum change in the vertical direction:
     \[
     p_y = m \cdot v_y
     \]
     where \( v_y = v \cdot \sin(\theta) \).

  2. The force applied to the post is the change in momentum over time:
     \[
     F = \frac{\Delta p_y}{\Delta t}
     \]

Using these steps, you can find the force applied to the post.

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### Question 5
- **Given:**
  - Mass of top (\( m \)) = 0.02 kg
  - Radius of the circular path (\( r \)) = 10.2 cm = 0.102 m
  - Linear velocity (\( v \)) = 2.41 m/s

- **Solution:**
  1. The angular momentum \( L \) is given by:
     \[
     L = m \cdot v \cdot r
     \]

Calculate \( L \) using this formula.

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### Question 6
- **Given:**
  - Mass of shirt (\( m \)) = 0.192 kg
  - Launch angle = 75.7°
  - Initial velocity (\( v \)) = 34.8 m/s
  - Gravitational acceleration (\( g \)) = 9.8 m/s²

- **Solution:**
  1. Calculate the time of flight by finding the vertical component of the initial velocity:
     \[
     v_y = v \cdot \sin(\theta)
     \]
  2. The time to reach the peak is \( t = \frac{v_y}{g} \).
  3. Total time of flight = \( 2t \).

After solving, you should find that the correct answer is:
- **(b) 2.16 seconds**

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Would you like detailed calculations for each step?

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### Related Questions
1. How do you calculate momentum in a collision scenario?
2. What is the significance of angular momentum in rotating objects?
3. How does the angle of launch affect the projectile's trajectory?
4. How can we determine the time of flight for an object thrown at an angle?
5. How does mass affect the angular momentum of a rotating object?

### Tip
When dealing with projectiles, always separate motion into horizontal and vertical components for easier calculations.

Explore solutions to physics problems involving momentum, angular momentum, and projectile motion. Questions cover concepts like force applied in collisions, angular momentum of a rotating object, and time of flight for projectiles. Ideal for Grades 11-12 students looking to deepen their understanding of physics.

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