To determine the horizontal distance traveled by the projectile, we can use the equations of projectile motion. Since air resistance is neglected, we can assume that the only force acting on the projectile is gravity.
Let's break down the given information:
- Initial velocity (muzzle speed): 980 m/s
- Launch angle: 30 degrees above the horizontal
To find the horizontal distance traveled, we need to calculate the time of flight (the time it takes for the projectile to hit the ground) and then multiply it by the horizontal component of the velocity.
- Calculate the time of flight: The time of flight can be found using the following formula: t = (2 * v * sin(theta)) / g
Where: t = time of flight v = initial velocity (muzzle speed) theta = launch angle g = acceleration due to gravity (approximately 9.8 m/s²)
Plugging in the values: t = (2 * 980 * sin(30°)) / 9.8
- Calculate the horizontal distance: The horizontal distance traveled can be found using the formula: d = v * cos(theta) * t
Where: d = horizontal distance traveled v = initial velocity (muzzle speed) theta = launch angle t = time of flight
Plugging in the values: d = 980 * cos(30°) * t
Now we can calculate the horizontal distance:
t = (2 * 980 * sin(30°)) / 9.8 t ≈ 100 seconds (rounded to two decimal places)
d = 980 * cos(30°) * t d ≈ 980 * 0.866 * 10 d ≈ 8,484 meters
Therefore, neglecting air resistance, the projectile will travel approximately 8,484 meters horizontally before striking the ground.