Question

A bullet fired into a plank loses half of its velocity after penetrating a thickness of 3cm. assuming that it has constant force of resistance, how much further does it penetrate before coming to rest

Answer 1

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Let the velocity of the bullet when it strikes the target be v.v.

Velocity after the bullet penetrated 15cm=v2.=v2.

Using v²=u²+2aSUsing v²=u²+2aS

(v2)2=v2+2a(15)(v2)2=v2+2a(15)

⟹v24=v2+30a⟹v24=v2+30a

⟹a=−v240⟹a=−v240

Since the resistance offered by the material to the bullet is same throughout, aaremains constant.

Using v²=u²+2aS for motion after 15cmUsing v²=u²+2aS for motion after 15cm

Finally the bullet is at rest, hence v=0v=0

Initial velocity for motion after 15cm =v2=v2

⟹(0)2=(v2)2+2(−v240)(S)⟹(0)2=(v2)2+2(−v240)(S)

⟹2(v240)(S)=(v2)2