A wooden block of length L and mass m is initially at rest o...

Question

A wooden block of length L and mass m is initially at rest on a smooth horizontal surface. A bullet, also of mass m, is fired horizontally with an initial velocity and passes completely through the block. The block moves forward a distance s. Assuming the bullet experiences a constant resistive force while passing through the block, what is the time it takes for the bullet to pass through the block?

To solve this problem, let's analyze the situation step by step:

Given parameters:

Mass of the block:

Mass of the bullet:

Initial velocity of the bullet:

Distance the block moves:

Length of the block:

The resistive force on the bullet is constant.

Equations of motion for the block:

When the bullet passes through the block, it exerts a constant force on the block. By Newton's Second Law, the acceleration of the block is:

From kinematic equations, the block moves forward a distance during the time :

Bullet's motion:

The bullet experiences a constant resistive force as it travels through the block. Its acceleration (negative, since it's decelerating) is:

Using the kinematic equation for the bullet:

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