Did you know?
Did you know that the acceleration of a cannon ball inside the barrel of a pirate ship's cannon can be calculated using the given information?
To find the acceleration, we can use the equation for acceleration, which is given by a = (v_f - v_i) / t, where v_f is the final velocity, v_i is the initial velocity, and t is the time taken.
Since the barrel of the cannon is 2 m long, we can use this distance as the displacement of the cannon ball. Assuming the cannon ball starts from rest at one end of the barrel, the initial velocity, v_i, would be 0 m/s.
We are given the muzzle velocity, which is the final velocity, v_f, and is equal to 350 m/s. However, we don't have the time taken, t, directly given.
To calculate the time taken, we can use the equation for average velocity, which is given by v_avg = Δx / t, where Δx is the displacement and t is the time taken. Rearranging the equation, we get t = Δx / v_avg.
Here, the displacement, Δx, is 2 m, as given, and the average velocity, v_avg, can be calculated by taking the average of the initial and final velocities. Since the initial velocity is 0 m/s and the final velocity is 350 m/s, the average velocity would be 175 m/s.
Substituting the values, t = 2 m / 175 m/s, we can calculate the time taken, which is approximately 0.011 seconds.
Now, we have all the necessary values to calculate the acceleration. Substituting v_f = 350 m/s, v_i = 0 m/s, and t = 0.011 s into the acceleration equation, we get:
a = (350 m/s - 0 m/s) / 0.011 s = 31818.18 m/s^2
Therefore, the acceleration of the cannon ball inside the barrel is approximately 31818.18 m/s^2.
Remember, acceleration is the rate at which an object changes its velocity, and in this case, the cannon ball gains considerable velocity within a short distance.
