In a ballistic pendulum a bullet of mass 10kg is fired horizontally with a speed into a large wooden stationary block of mass 2kg that is suspended vertically by two cords as shown with a figure( not drawn) . In very short time the bullet penetrates the pendulum and remains embedded. The entire system tries to swing through a maximum height of 10m.

Question

Find the relation that gives the speed V and In terms of the height and then find its value.

Answer 1

First, we need to apply the principle of conservation of momentum. Since the bullet is fired horizontally, the initial momentum of the system is simply the momentum of the bullet, which is given by:

p_initial = m_bullet * v

where m_bullet is the mass of the bullet and v is its velocity. Since the bullet remains embedded in the pendulum, the final momentum of the system is simply the momentum of the pendulum after it has reached its maximum height. At this point, the pendulum is momentarily stationary (i.e. its velocity is zero) and all of its energy is potential energy. Thus, the final momentum of the system is zero.

Applying the principle of conservation of momentum, we can equate the initial and final momenta:

m_bullet * v = 0

Solving for v, we get:

v = 0 / m_bullet = 0

This means that the speed of the bullet is zero, which is obviously not possible. Therefore, there must be some mistake in the problem statement or the values given. Please double-check the information and provide any additional details if possible.