Question

An experiment is done to compare the initial speed of bullets fired from different handguns: a 9.0 mm and a .44 caliber. The guns are fired into a 10-kg pendulum bob of length L. Assume that the 9.0-mm bullet has a mass of 6.0 g and the .44-caliber bullet has a mass of 12 g . If the 9.0-mm bullet causes the pendulum to swing to a maximum angular displacement of 4.3∘ and the .44-caliber bullet causes a displacement of 10.1∘ , find the ratio of the initial speed of the 9.0-mm bullet to the speed of the .44-caliber bullet, (v0)9.0/(v0)44. I have attach below the equation

(osos – 1) 767/(* + 1) = oa

Answer 1

let M = 10 kg

for 9mm bullet,
m1 = 6.0 g = 0.006 kg
theta1 = 4.3 degrees
vo1 = (1 + M/m1)*sqrt(2*g*L*(1 - cos(theta1) )

for 0.44 caliber
m2 = 12 g = 0.012 kg
theta2 = 10.1 degrees
vo2 = (1 + M/m2)*sqrt(2*g*L*(1 - cos(theta2) )

vo1/vo2 = ((m1 + M)/(m2 + M))*sqrt((1 - cos(theta1))/(1 - cos(theta2) ) )

= (0.006 + 10)/(0.012 + 10)*sqrt( (1 - cos(4.3))/(1 - cos(10.1) ) )

= 0.886 <<<<<<<<--------------Answer