Final answer:
The cannonball will hit the ground approximately 1111 meters away from the cannon.
Step-by-step explanation:
To calculate the horizontal distance the cannonball will travel, we can use the horizontal component of its initial velocity. The horizontal component can be found using the formula:
Horizontal component of velocity = initial velocity * cos(angle)
Using the given initial velocity of 105 m/s and the angle of 26 degrees, we can calculate:
Horizontal component of velocity = 105 m/s * cos(26) = 94.24 m/s
To find the time of flight, we can use the equation:
Time of flight = (2 * initial velocity * sin(angle)) / g
Where g is the acceleration due to gravity (approximately 9.8 m/s²). Plugging in the values:
Time of flight = (2 * 105 m/s * sin(26)) / 9.8 m/s² = 11.78 s
The horizontal distance the cannonball will travel is given by:
Distance = horizontal component of velocity * time of flight
Distance = 94.24 m/s * 11.78 s ≈ 1111 m