The cannon on a pirate ships shoots cannon balls with a speed of 350m/s (the muzzle velocity). The cannon can be adjusted to shoot at any elevation above the horizontal. If the cannon’s barrel is 2m long and the force on the cannon ball is constant, what is the acceleration of the cannon ball in m/s^2 inside the barrel?
To find the acceleration of the cannonball inside the barrel, we need to determine the time it takes for the cannonball to travel the length of the barrel.
Using the equation of motion for constant acceleration: \[v = u + at,\]
where:
- \(v\) is the final velocity (muzzle velocity) = 350 m/s,
- \(u\) is the initial velocity (0 m/s, as the cannonball is initially at rest inside the barrel),
- \(a\) is the acceleration, and
- \(t\) is the time taken to travel the distance (length of the barrel) = 2 m.
Plugging in the values, we have:
\[350 = 0 + 2a.\]
Simplifying the equation, we find:
\[a = \frac{350}{2} = 175 \, \text{m/s}^2.\]
Therefore, the acceleration of the cannonball inside the barrel is \(175 \, \text{m/s}^2\).