An experiment is done to compare the initial speed of bullets fired from differe

Question

An experiment is done to compare the initial speed of bullets fired from different handguns: a 9 { m mm} and a .44 caliber. The guns are fired into a 10- kg pendulum bob of length L. Assume that the 9 mm bullet has a mass of 6 g and the .44-caliber bullet has a mass of 12 g . If the 9 mm bullet causes the pendulum to swing to a maximum angular displacement of 4.3 degrees and the .44-caliber bullet causes a displacement of 10.1 degrees , find the ratio of the initial speed of the 9 mm bullet to the speed of the .44-caliber bullet, (v_0)_9 mm/(v_0)_44_caliber.

So the equation I got for v_0 is:::

v_0 = ((M+m)/m ) *(sqrt(2*g*L(1-cos(theta)))

I know this is correct from a previous question. It seems like I should just be able to plug the numbers for each gun, the 9 mm and the 44 caliber gun. But how do I solve for the length of the arm of the pendulum L?

Or am I just way off?

Explanation / Answer

v_0 = ((M+m)/m ) *(sqrt(2*g*L(1-cos(theta))) you r asked for the ratio of v1/v2 so v1/v2=[(10+.006)/.006]/[(10+.012)/.012] *sqrl((1-cos(4.3)/(1-cos(10.1)) =.851

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