When a bullet leaves a barrel of a rifle, it is moving 640 m/s. If the barrel is 1.20 m long, and if the bullet undergoes constant acceleration while within the barrel, how long after the rifle is fired will the bullet emerge from the end of the barrel?
a=(V^2-Vo^2)/2d = (640^2-0)/2.4=170,667
m/s^2.
V = Vo + a*t
t=(V-Vo)/a = (640-0)/170,667=0.00375 s.
= 3.75 ms.
To determine the time it takes for the bullet to emerge from the end of the barrel, we can use the equation of motion with constant acceleration. The equation is given by:
v = u + at
Where:
v = final velocity (640 m/s)
u = initial velocity (0 m/s inside the barrel, as the bullet starts from rest)
a = acceleration (unknown in this case, as it is not mentioned)
t = time (unknown)
Since the bullet undergoes constant acceleration while inside the barrel, we can use the formula for uniform acceleration:
v^2 = u^2 + 2as
Where:
s = displacement (length of the barrel, 1.20 m)
Assuming the acceleration is constant, we can rearrange the equation to solve for acceleration:
a = (v^2 - u^2) / (2s)
Substituting the given values:
a = (640^2 - 0^2) / (2 * 1.20)
Simplifying the equation:
a = 276800 / 2.40
a = 115333.33 m/s^2
Now, we can use the equation of motion to find the time (t) it takes for the bullet to emerge from the end of the barrel:
640 = 0 + (115333.33)t
Simplifying the equation:
t = 640 / 115333.33
t ≈ 0.0055 seconds
Therefore, it will take approximately 0.0055 seconds (or 5.5 milliseconds) for the bullet to emerge from the end of the barrel after the rifle is fired.