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### Muzzle Speed

```
Date: 03/21/2002 at 22:27:11
From: Jaime
Subject: Physics

A 15-gram bullet strikes and becomes embedded in a 1.10 kg block of
wood placed on a horizontal surface just in front of the gun. If the
coefficient of friction between the block and the surface is .25 and
the impact drives the block 9.5 meters before it comes to rest, what
was the muzzle speed of the bullet?
```

```
Date: 03/22/2002 at 09:28:12
From: Doctor Ian
Subject: Re: Physics

Hi Jaime,

There are two things going on here. The first is that the bullet
transfers its momentum to the block. That is,

momentum of bullet before = momentum of bullet and block after

Now, this doesn't help you unless you know one of the speeds involved.
Fortunately, you know that the block starts sliding with some initial
velocity, v0; and there is a force acting to slow it down; and it
comes to a rest after some point.

This is exactly the same situation you get when you throw a ball into
the air, and gravity slows it down until it pauses for a moment at the
top of its trajectory, except you have a frictional force instead of a
gravitational force, and the direction is horizontal instead of
vertical.

Think about how you would solve the problem for the ball (i.e., if it
reaches a certain height before stopping, what was the initial upward
velocity), and use that same approach to find the initial velocity of
the block.

Once you have the initial velocity of the block, you can use
conservation of momentum to deduce the velocity of the bullet when it
hit the block.

Does this help?

- Doctor Ian, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
High School Physics/Chemistry

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