A bullet is fired a plank of wood with a speed of 200m/s. After passing through the plank, its speed reduces to 180m/s. Another bullet identical with a speed of 100m/s is fired at the same plank. What is the speed of this bullet after passing through the plank. (resistance offered by the plank is the same for both bullets)
To find the speed of the second bullet after passing through the plank, we can use the concept of conservation of momentum.
Conservation of momentum states that the total momentum of a system remains constant if there are no external forces acting on it. In this case, we can assume that the only external force acting on the system is the resistance offered by the plank, which is the same for both bullets.
The momentum of an object is given by the product of its mass and velocity. Since both bullets are identical, they have the same mass. Let's assume the mass of each bullet is represented by 'm'.
For the first bullet:
Initial momentum = mass * initial velocity
Final momentum = mass * final velocity
Using the given information:
Initial momentum = mass * initial velocity = m * 200
Final momentum = mass * final velocity = m * 180
For the second bullet:
Initial momentum = mass * initial velocity = m * 100
Final momentum = ?
Since the system is isolated, the total initial momentum of the system should be equal to the total final momentum of the system. Therefore, we can set up an equation:
(m * 200) + (m * 100) = (m * 180) + Final momentum
Simplifying the equation, we have:
300m = 180m + Final momentum
Subtracting 180m from both sides:
120m = Final momentum
Therefore, the speed of the second bullet after passing through the plank is 120 m/s.