Question

A bullet of mass m = 8.00 g is fired into a block of mass M = 210 g that is initially at rest at the edge of a table of height h = 1.00 m (see figure below). The bullet remains in the block, and after the impact the block lands d =  1.90 m from the bottom of the table. Determine the initial speed of the bullet.

________m/s

Answer 1

Given:

Mass of the bullet,

Mass of the block,

Initial velocity of the block,

Height of the table,

Horizontal distance covered by the bullet-block system after the collision,

Let be the initial speed of the bullet

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First, find the time taken by the bullet-block to hit the bottom.

Consider the vertical motion of the bullet-block system

Use formula

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Consider the horizontal motion of the bullet-block system

There is no acceleration in horizontal direction, so horizontal velocity remains constant.

Horizontal velocity = Horizontal distance/Time

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Velocity of bullet-block system after the collision

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Initial speed of the bullet

Consider the collision between the bullet and the block

During collision momentum is conserved

Initial momentum = Final momentum

ANSWER:

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