With the given information, fill in the blank boxes. (the components of velocity, total time in the air, maximum height, and horizontal displacement when hitting the ground )

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With the given information, fill in the blank boxes. (the components of velocity, total time in the air, maximum height, and horizontal displacement when hitting the ground )

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**Projectiles**

**Comparison of Trajectories at Various Launch Angles**

This table details the trajectory characteristics of a projectile launched at different angles with a constant velocity.

| **Velocity (m/s)** | **Angle (°)** | **\(v_h\) (m/s)** | **\(v_v\) (m/s)** | **Time (s)** | **Max \(Δd_v\) (m)** | **\(Δd_h\) (m)** |
|:------------------:|:-------------:|:-----------------:|:----------------:|:------------:|:--------------------:|:----------------:|
| 40.0               | 15.0          | 34.6              |                  |              |                      |                  |
| 40.0               | 30.0          | 34.6              | 20               | 4.0          | 20m                  | 138              |
| 40.0               | 45.0          | 34.6              |                  |              |                      |                  |
| 40.0               | 60.0          | 34.6              |                  |              |                      |                  |
| 40.0               | 75.0          | 34.6              |                  |              |                      |                  |

**Key:**
- **Velocity (m/s):** The speed at which the projectile is launched.
- **Angle (°):** The angle of launch above the horizontal.
- **\(v_h\) (m/s):** The horizontal component of the velocity.
- **\(v_v\) (m/s):** The vertical component of the velocity.
- **Time (s):** The total time of flight.
- **Max \(Δd_v\) (m):** The maximum vertical displacement.
- **\(Δd_h\) (m):** The horizontal range.

**Diagram Explanation:**
The table illustrates the relationship between launch angle and various trajectory parameters while keeping the launch velocity constant. Only one complete set of data is provided for a launch angle of 30 degrees, showing specific values for vertical velocity component, time of flight, maximum vertical displacement, and horizontal range. Further data would be needed to complete the analysis for other angles.

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Transcribed Image Text:--- **Projectiles** **Comparison of Trajectories at Various Launch Angles** This table details the trajectory characteristics of a projectile launched at different angles with a constant velocity. | **Velocity (m/s)** | **Angle (°)** | **\(v_h\) (m/s)** | **\(v_v\) (m/s)** | **Time (s)** | **Max \(Δd_v\) (m)** | **\(Δd_h\) (m)** | |:------------------:|:-------------:|:-----------------:|:----------------:|:------------:|:--------------------:|:----------------:| | 40.0 | 15.0 | 34.6 | | | | | | 40.0 | 30.0 | 34.6 | 20 | 4.0 | 20m | 138 | | 40.0 | 45.0 | 34.6 | | | | | | 40.0 | 60.0 | 34.6 | | | | | | 40.0 | 75.0 | 34.6 | | | | | **Key:** - **Velocity (m/s):** The speed at which the projectile is launched. - **Angle (°):** The angle of launch above the horizontal. - **\(v_h\) (m/s):** The horizontal component of the velocity. - **\(v_v\) (m/s):** The vertical component of the velocity. - **Time (s):** The total time of flight. - **Max \(Δd_v\) (m):** The maximum vertical displacement. - **\(Δd_h\) (m):** The horizontal range. **Diagram Explanation:** The table illustrates the relationship between launch angle and various trajectory parameters while keeping the launch velocity constant. Only one complete set of data is provided for a launch angle of 30 degrees, showing specific values for vertical velocity component, time of flight, maximum vertical displacement, and horizontal range. Further data would be needed to complete the analysis for other angles. ---
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