What is the equation to solve for muzzle speed in a ballistic pendulum problem?

[scheng12]

Homework Statement

During a summer internship with a company, you devised the following method of measuring the muzzle speed of a high-powered rifle, as shown in the figure. You fire a bullet into a rod of mass 5.5 kg and length 150 cm that is free to rotate about the pivot at the top. The bullet, whose mass is 8.55 g, strikes at the center of mass of the rod and remains embedded. You measure the maximum opening angle to be 11.5 degrees. What is the muzzle speed in m/s?

Homework Equations

I know the equation to solve for the muzzle speed for a normal ballistic pendulum is

v₀=(M+m)[tex]\sqrt{}2gL(1-cos\vartheta)[/tex]/m

The Attempt at a Solution

When I plug the values in the answer comes out to be false since the bullet hits the rod in the center, instead of at the tip. I also tried to plug in L/2 but that doesn't work either. Any ideas?

 

[BMWPower06]

any1?

 

[omegacore]

Instead of just applying the formula you might want to consider where the formula comes from.

A simple energy relationship will tell you that your square root is in the wrong place.

L = L(overall)/2 this is correct.

 

[BMWPower06]

where is the square root supposed to be?

 

[omegacore]

The square root should be over everything on the right hand side.