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The problem describes a projectile motion scenario where a cannonball is fired at an angle of \(44^\circ\) from the horizontal with an initial velocity of 790 feet per second. We need to find the horizontal distance (range) the cannonball will travel, assuming the initial height is 0 feet and air resistance is negligible.

### Steps to solve:

1. **Horizontal and vertical components of velocity:**
   The initial velocity (\(v_0 = 790\) feet/second) can be split into horizontal and vertical components using the given angle (\(\theta = 44^\circ\)):

   \[
   v_{0x} = v_0 \cdot \cos(\theta)
   \]
   \[
   v_{0y} = v_0 \cdot \sin(\theta)
   \]

2. **Time of flight:**
   The time of flight \(T\) can be found using the vertical motion, where the vertical displacement is 0 (since the cannonball starts and ends at the same height). The formula for the time of flight is:

   \[
   T = \frac{2 v_{0y}}{g}
   \]
   where \(g = 32.2\) feet/second\(^2\) is the acceleration due to gravity.

3. **Horizontal distance (range):**
   The horizontal distance (range) \(R\) is given by:

   \[
   R = v_{0x} \cdot T
   \]

Let's calculate this now.The cannonball will travel approximately **19,370 feet** horizontally.

Would you like more details on the calculations or have any further questions?

Here are 5 related questions to expand on this topic:
1. How would the horizontal distance change if the angle of launch was increased to 60°?
2. What would happen to the range if the initial velocity was doubled?
3. How would air resistance affect the motion of the projectile?
4. What is the maximum height the cannonball reaches during its flight?
5. How does the launch angle affect both the time of flight and range of the projectile?

**Tip:** The optimal angle for maximum range in projectile motion without air resistance is \(45^\circ\).

A cannon is fired at an angle of 44° with the horizontal. If the cannonball has an initial velocity of 790 feet per second, how far (horizontally) will the shot travel? Assume the initial height of the projectile is 0 feet, and neglect air resistance.

Explore how to calculate the horizontal distance traveled by a cannonball fired at a 44° angle with an initial velocity of 790 feet per second. This problem covers key concepts in projectile motion, trigonometry, and kinematics, suitable for high school and college-level physics.

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