A stray bullet from the Parisian ISIS terrorist attack sticks to a hanging cale

Question

A stray bullet from the Parisian ISIS terrorist attack sticks to a hanging cale sign which says "Je suis Charlie Hebdo". The bullet has velocity 150m/s and mass 200g, the sign has a mass of 4kg. They move together after the collision. A CCTV security camera showed that the height of the sign after it was struck was the same height of another terrorist standing close-by. Find the height of the sign (and bullet) after the collision from the equilibrium height before the incident. What angle was formed by the cable?. If the sign was originally 4m from the ground, what height do you compute for the height of the other terrorist was so that you can tell the Paris Gendarmes?

Explanation / Answer

no external force so for system of bullet and sign linear momentum will be conserved

200/1000 *150 = (4200)/1000 V

V= 7.14285714286 m/s

after bullet has penetrated into box no energy will be wated and it will perform pendulum oscillation

4200/1000 *9.81* h = 0.5 * 4200/1000 * V^2

h=2.60042855063 m

so height of tourist = 4+2.60042855063 =6.60042855063 m

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