A BULLET FIRED INTO A FIXED TARGET LOSES HALF OF ITS VELOCITY AFTER PENETRAATING 3 CM. HOW MUCH FURTHER IT WILL PENETRATE BEFORE CONING TO REST ASSUMING THAT IT FACES CONSTANT RESISTANCE TO MOTION.

The bullet loses half its velocity after penetrating 3 cm into the target.

Let us say that the gun fires the bullet with force F.

 

The work done by the gun goes as change in kinetic energy of the bullet.

 

Thus, work done after penetrating 3 cm inside the target is

 

F × (3 cm) = ½mv² - ½m(v/2)² = 3/8 mv²

 

Thus, we have

 

mv² = 8F

 

Now, when the bullet penetrates further distance x, the entire kinetic energy is lost. Thus, we have

 

F × (3 + x cm) = ½mv²

 

Thus, the distance x further penetrated by the bullet inside the target is,