A machine gun fires 10 rounds per second. The speed of the bullets is 300 m/s. What is the distance in the air between the flying bullets?

I'll assume you mean to say the horizontal distance between them.

After the bullets are launched from the gun, their horizontal motion is constant (idealized projectile motion).

We know that one bullet is fired every #0.1# #"s"#, so we essentially need to find the horizontal distance a bullet would travel in #0.1# #"s"# with the given initial speed.

To do this, we use the equation

#ul(Deltax = v_(0x)t#

where

• #Deltax# is the change in #x#-position, which is equal to the distance between bullets

• #v_(0x)# is the initial horizontal speed of the bullet (#300# #"m/s"#)

• #t# is the time interval (#0.1# #"s"#)

Plugging in values:

#overbrace(color(red)(Deltax))^"distance" = (300color(white)(l)"m/s")(0.1color(white)(l)"s") = color(red)(ulbar(|stackrel(" ")(" "30color(white)(l)"m"" ")|)#

Each round travels for the duration of .1 seconds before the next is fired, as the firing rate is 10 rounds per second, or #1/10# seconds per round.

Our answer is the distance a bullet travels while moving at 300m/s for .1 seconds.

300 meters per second times .1 seconds is 30 meters.

Therefore, the bullets are 30 meters apart.