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The problem asks to determine all unknowns for a cannonball launched vertically upwards with an initial velocity of 50.0 m/s.

### The given information:
- **Initial velocity** = 50.0 m/s (this is the velocity at launch)
- **Gravity** \(g\) = 9.81 m/s² (as indicated)

### 1. **Initial Velocity (Overall)**: 
The overall initial velocity is given as 50.0 m/s.

### 2. **Initial Horizontal Velocity**:
Since the cannonball is launched vertically, there is no horizontal component to the velocity. Therefore, the **initial horizontal velocity** is:
\[ v_{\text{horizontal}} = 0 \, \text{m/s} \]

### 3. **Initial Vertical Velocity**:
Since the launch is purely vertical, the **initial vertical velocity** is the same as the overall initial velocity, which is:
\[ v_{\text{vertical}} = 50.0 \, \text{m/s} \]

### Final values:
- **Initial velocity**: 50.0 m/s
- **Initial horizontal velocity**: 0 m/s
- **Initial vertical velocity**: 50.0 m/s

Would you like further details, or do you have any questions on how these values were determined?

### Expansion Questions:
1. What would be the maximum height reached by the cannonball?
2. How long will it take for the cannonball to reach its maximum height?
3. How much time will it take for the cannonball to return to the ground?
4. What is the total distance traveled by the cannonball during its flight?
5. How would air resistance affect the motion of the cannonball?

### Tip:
Remember, when an object is launched vertically, the only force acting on it (ignoring air resistance) is gravity, which affects the vertical motion and not the horizontal motion.

A cannonball is launched vertically upwards with an initial velocity of 50.0 m/s. Determine all unknowns.

Learn how to determine the initial horizontal and vertical velocities for a cannonball launched vertically upwards with an initial velocity of 50.0 m/s. This problem covers kinematic equations and projectile motion concepts, suitable for high school physics students in Grades 9-12.

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