What Is the Initial Velocity of the Bullet Before Impact?

[lizzy2k6]

Lets assume that a signature of guns is the velocity of its built. A built mass is 2g in average and very close in different guns. You are the detective assigned for a crime scene investigation. You realize that there has been a shooting involved. The built has made a whole 0.30m deep in the wall. If the resistive force of the wall on the built is 900N. You also realize that a 5kg sign hanging from the ceiling has a dent on it and has made a small scratch on the wall. If the gun was shot parallel to the wall what is the velocity of the built before hitting the sign?


I have no clue where to start or even what the question is asking...any help at all would be really appreciated. Thanks.

The attachment is the original problem with figures.

 

[Andrew Mason]

The object whose speed you are trying to find is the BULLET. The bullet hits the sign and moves it so that it just grazes the wall. The bullet then loses the rest of its kinetic energy in the wall. When the bullet moves the sign, the sign's centre of mass rises.

The loss of energy in the wall is simple. That gives you the speed after hitting the sign. The sign motion is the result of a transfer of energy from the bullet to the sign. You can work that out if you have the distance to the wall (which I expect is in your diagram) from which you can work out the increase in potential energy of the sign at its highest point.

The loss of energy in the wall and to the sign gives you the original bullet energy. Work out its speed from that.

AM