Question

Q-1 A bullet is moving at the late of 250 m/s, is fired in to a log of wood. The bullet penetratesto a depth of 40cm. If the bulet Roving with the same velocity is fired in to a similar piece ofwood 20 cm thick, with what velocity would it emerge? Take the resistance to be uniform in boththe cases.​

Answer 1

The bullet would emerge from the wood with a velocity of 2.8 m/s in both cases.

Step-by-step explanation:

To find the velocity with which the bullet would emerge from the wood of 20 cm thickness, we can use the concept of work-energy theorem. The work done by the resistance force on the bullet is equal to the change in kinetic energy of the bullet. Since the resistance force is uniform in both cases, the work done is the same in both cases. Therefore, the change in kinetic energy is the same in both cases, which means the final velocity of the bullet will be the same in both cases.

So, if the bullet penetrates to a depth of 40 cm in the first case, it will also penetrate to a depth of 40 cm in the second case. The velocity with which the bullet emerges from the wood is given by the equation:

v = sqrt(2gh)

where v is the velocity, g is the acceleration due to gravity, and h is the depth to which the bullet penetrates. Plugging in the values, we get:

v = sqrt(2 * 9.8 * 0.4) = 2.8 m/s

Therefore, the bullet would emerge from the wood with a velocity of 2.8 m/s in both cases.

Answer 2

The bullet would emerge from the wood with the same initial velocity of 250 m/s.

Step-by-step explanation:

To determine the velocity with which the bullet would emerge from a similar piece of wood 20 cm thick, we can use the conservation of energy principle. Since the resistance is uniform in both cases, the work done by the bullet to penetrate the wood is equal to the work done by the wood to slow down and stop the bullet.

The work done by the bullet to penetrate the wood can be calculated as:

Work = force x distance

The velocity at which the bullet emerges from the wood can be determined using the equation:

Work = force x distance = 0.5 x mass x velocity^2

Simplifying the equation, we get:

velocity = sqrt(2 x Work / mass)

Substituting the known values, we have:

velocity = sqrt(2 x (0.5 x mass x initial_velocity^2) / mass)

Therefore, the bullet would emerge from the wood with the same initial velocity of 250 m/s.