A 75.0 g bullet is fired at a muzzle velocity of 476 m/s from a gun with a mass 4.75 kg and a barrel length of 60 cm
How long is the bullet in the barrel?
d = V*t.
t = d/V = 0.60m/476 = 1.26*10^-3 s.
To find the time it takes for the bullet to travel through the barrel, we can use the formula of motion:
v = u + at
Where:
v = final velocity (muzzle velocity of the bullet) = 476 m/s
u = initial velocity (0 m/s, since the bullet starts from rest inside the barrel)
a = acceleration (which will be determined)
t = time taken
To find 'a', we can use the formula:
a = (v - u) / t
Substituting the given values:
476 m/s = (0 m/s) + a * t
a = 476 m/s / t
Now, let's find the acceleration in terms of distance:
We can use the formula of motion:
s = ut + 0.5 * a * t^2
Where:
s = distance (length of the barrel) = 60 cm = 0.6 m
u = initial velocity (0 m/s, since the bullet starts from rest inside the barrel)
a = acceleration (which we found earlier in terms of distance)
t = time taken
Plugging in the values, the equation becomes:
0.6 m = 0 * t + 0.5 * (476 m/s / t) * t^2
0.6 = 238t
t = 0.6 / 238
Simplifying, we get:
t ≈ 0.0025 seconds
Therefore, the bullet is in the barrel for approximately 0.0025 seconds.
To determine the length of time the bullet is in the barrel, we need to use the equation for average speed:
Average Speed = Distance / Time
In this case, the distance is the length of the barrel and the average speed is the muzzle velocity of the bullet. Therefore, we can rearrange the equation to solve for time:
Time = Distance / Average Speed
Given that the muzzle velocity of the bullet is 476 m/s and the barrel length is 60 cm (which is equal to 0.6 m), we can substitute these values into the equation to find the time:
Time = 0.6 m / 476 m/s
Calculating this:
Time = 0.00126 seconds
Therefore, the bullet is in the barrel for approximately 0.00126 seconds.