A bullet moving at a speed of 154 m/s passes through a plank of wood. After passing through the plank, its speed is 149 m/s. Another bullet, of the same mass and size but moving at 91 m/s, passes through an identical plank. What will this second bullet's speed be after passing through the plank? Assume that the resistance offered by the plank is independent of the speed of the bullet.
To determine the second bullet's speed after passing through the plank, we can use the principle of conservation of momentum.
The momentum of an object is defined as the product of its mass and velocity. According to the principle of conservation of momentum, the total momentum of an isolated system remains constant if no external forces act on it. In this case, we can consider the bullet-plank system as an isolated system.
Let's denote the mass of each bullet as "m" and their initial velocities as "v1" and "v2" respectively. The first bullet has an initial velocity of 154 m/s and a final velocity of 149 m/s after passing through the plank. The second bullet has an initial velocity of 91 m/s. We need to find the final velocity of the second bullet after passing through the plank, which we'll denote as "v3".
According to the law of conservation of momentum, the initial momentum of the system is equal to the final momentum.
The initial momentum of the system can be calculated by multiplying the mass of the first bullet with its initial velocity:
Initial momentum (before collision) = m * v1
The final momentum of the system can be calculated by adding the final momentum of the first bullet and the final momentum of the second bullet:
Final momentum (after collision) = (m * v2) + (m * v3)
Based on the conservation of momentum, we can set the initial momentum equal to the final momentum:
m * v1 = (m * v2) + (m * v3)
To find v3, we need to rearrange the equation:
v3 = (m * v1 - m * v2) / m
Simplifying the expression:
v3 = v1 - v2
Substituting the given values:
v3 = 154 m/s - 91 m/s
v3 = 63 m/s
Therefore, the second bullet's speed after passing through the plank will be 63 m/s.