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/s2 inside the barrel?
The previous answer is incorrect. Here's the correct solution.
The muzzle velocity is 350 m/s and the distance covered (x) is 2m.
So from the known variables,
displacement (s) = 2m.
initial velocity (u) = at rest (0 m/s).
final velocity at end of 2m (v) (before shooting) = 350 m/s.
acceleration (a) = ?
time (t) = ?
So we use the kinematics equation: v^2 = u^2 + 2as.
Rearranging the equation:
a = (v^2 - u^2) / 2s.
Now, just plug in the values to get the final answer for a in m/s.
HINT: It should be about 3zzzz m/s.
Hope this helps!!
Well, with a muzzle velocity of 350m/s, it seems like that cannonball has places to be! Now, let's calculate its acceleration while it's inside the barrel, shall we?
To find the acceleration, we need to determine the time it takes for the cannonball to travel the length of the barrel. We can use the equation: v = d/t, where v is the velocity, d is the distance, and t is the time.
In this case, the velocity is 350m/s, and the distance is the length of the barrel, which is 2m. Rearranging the equation, we have t = d/v.
Therefore, the time it takes for the cannonball to travel the length of the barrel is t = 2m / 350m/s, which gives us around 0.0057 seconds.
Now, we can calculate the acceleration using the equation: a = Δv/Δt, where Δv is the change in velocity and Δt is the change in time.
Since the cannonball starts from rest inside the barrel, the change in velocity is the final velocity, which is 350m/s, minus the initial velocity, which is 0m/s. So Δv = 350m/s - 0m/s = 350m/s.
Similarly, the change in time is the final time, which is 0.0057 seconds, minus the initial time, which is 0 seconds. So Δt = 0.0057s - 0s = 0.0057s.
Plugging these values into the formula, we get a = 350m/s / 0.0057s, which gives us an acceleration of approximately 61403.5 m/s².
So, inside the barrel, that cannonball accelerates like a thunderbolt!
To find the acceleration of the cannonball inside the barrel, we can use the equation:
v^2 = u^2 + 2as
where:
v = final velocity of the cannonball (350 m/s)
u = initial velocity of the cannonball (0 m/s, since it starts from rest)
a = acceleration of the cannonball
s = distance traveled by the cannonball inside the barrel (2 m)
Plugging in the values into the equation:
350^2 = 0^2 + 2a(2)
122,500 = 4a
Divide both sides of the equation by 4:
a = 122,500 / 4
a = 30,625 m/s^2
Therefore, the acceleration of the cannonball inside the barrel is 30,625 m/s^2.
To find the acceleration of the cannonball inside the barrel, we need to use the formula for acceleration:
acceleration = change in velocity / time
In this case, the cannonball starts from rest inside the barrel and reaches a velocity of 350 m/s at the muzzle. The change in velocity is therefore 350 m/s - 0 m/s = 350 m/s.
Now, we need to find the time it took for the cannonball to reach this velocity. To do this, we can use the physics equation:
final velocity = initial velocity + acceleration * time
We know that the initial velocity is 0 m/s and the final velocity is 350 m/s. Rearranging the equation, we have:
time = (final velocity - initial velocity) / acceleration
Substituting the values, we get:
time = (350 m/s - 0 m/s) / acceleration
Since the length of the cannon's barrel is 2 m, and we know that velocity = distance / time, we can write:
350 m/s = (2 m) / time
Solving for time, we get:
time = (2 m) / 350 m/s = 0.0057 s
Now, we can substitute the time value back into the equation for acceleration:
acceleration = (final velocity - initial velocity) / time
= (350 m/s - 0 m/s) / 0.0057 s
Calculating this, we find:
acceleration = 61403 m/s^2
Therefore, the acceleration of the cannonball inside the barrel is approximately 61403 m/s^2.
average velocity in the barrel is ... (0 + 350) / 2 = 175 m/s
time in the barrel is ... 2 m / 175 m/s
acceleration is ... 350 m/s / (time in barrel)