Problem $2$

In the forensic analysis lab, a Morgan State University law enforcement officer is testing the speed of several bullets fired at various targets for accuracy. As shown in the diagram, a bullet of mass $10$ grams is shot into a suspended block of wood of mass of $2$ kg $.$ When the bullet hits the block, it is embedded in the block thus causing the block to swing upward, reaching a height of $5$ cm $.$

A$.$ Using the conservation of linear momentum and conservation of mechanical energy of the system, determine the initial speed of the bullet.

$[6$ points$]$

B$.$ Determine the change in the kinetic energy of the system resulting from the collision.

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