A bullet is fired into a wall lose a half of its velocity after penetrating 3 cm. Further how much can it penetrate.

Asked by acv27joy | 25th May, 2018, 10:06: PM

Expert Answer:

Equation of motion to be used :- " v2 = u2-2aS" , v and u are final and intial speed respectively, a is retardation and S is distance.
Half of the speed lost in 3 cm. if initial speed is v, then after travelling 3 cm in wall final speed becomes v/2
hence v2/4 = v2-2×a×0.03 ......(1)
solving for retardation a from eqn(1) , we write retardation a in terms of v , hence  a = 12.5×v2
to stop the bullet completely, we need to consider that final speed of bullet is zero and initial speed v/2.
hence the further stopping distance S is calculated as  0 = (v2/4)-2×(12.5V2)×S...............(2)
solving eqn. (2) for S, we get S = 0.01 m = 1 cm.
hence bullet will travel further 1 cm and will be stopped completely.

Answered by Thiyagarajan K | 26th May, 2018, 09:27: AM

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