the paris gun of world war I was a super gun capable of firing a 234lb shell about 81 miles away. these shells are also the first man made objects to make it to a stratosphere. the length of the barrel of one of these guns was about 34 mETers. a projectile fired from a paris gun could reach a velocity of 1640 m/s by the time it left the barrel. what is the acceleration of the projectile in the barrel?
recall that
v^2 = 2as
You have v and s.
To determine the acceleration of the projectile in the barrel, we need to use the kinematic equation:
v^2 = u^2 + 2as
Where:
- v is the final velocity (1640 m/s in this case)
- u is the initial velocity (which we assume to be 0 m/s since the shell starts from rest)
- a is the acceleration of the projectile in the barrel (what we want to find)
- s is the distance traveled in the barrel (the length of the barrel, given as 34 meters)
Rearranging the equation, we have:
a = (v^2 - u^2) / (2s)
Plugging in the values:
a = (1640 m/s^2 - 0 m/s^2) / (2 * 34 m)
Simplifying:
a = 1640 m/s^2 / 68 m
Calculating:
a ≈ 24.12 m/s^2
Therefore, the acceleration of the projectile in the barrel is approximately 24.12 m/s^2.