To find the distance between the holes in the target, we can use the fact that the horizontal velocity of the bullets remains constant throughout their motion.
Let's consider the first bullet with a horizontal velocity of 320 m/s. Since the bullet is fired horizontally, its initial vertical velocity is 0 m/s. We can use the equation:
distance = velocity * time
The time it takes for the first bullet to reach the target can be calculated as:
time = distance / velocity
Substituting the values, we have:
time = 50 m / 320 m/s = 0.15625 s
During this time, the first bullet travels a horizontal distance of 50 m.
Now, let's consider the second bullet with a horizontal velocity of 350 m/s. Using the same equation, we can calculate the time it takes for the second bullet to reach the target:
time = 50 m / 350 m/s = 0.142857 s
During this time, the second bullet travels a horizontal distance of 50 m.
Therefore, both bullets hit the target at the same horizontal position, 50 m away from the firing point. Consequently, the distance between the holes in the target is 50 meters.