Question

A bullet is fired normally on an immovable wooden plank. it loses 25% of its momentum in penetrating a thickness 3.5cm of the plank. what is the total thickness penetrated by the bullet.

Answer 1

Take initial momentum (Pi)= mv
as the momentum is dropped by 25 percent, the final momentum will be

Pi-(25/100)Pi=(3/4)Pi=Pf

assuming that the mass is constant,

pf =3/4 mv = m (3/4 v)

velocity after travelling 3.5 cm = 3/4 v

from equation v²-u²=2as

(3/4)² v²-v² = 2a (3.5)

[9/16 v² - v²] / 2(3.5) = a

(-7/16 v²)/7 = a

a= -1/16 v²

now to find displacement at velocity=0

0²-v² = 2 (-1/16v²) s
1= (1/8) s

s= 8 cm

Answer 2

Answer:

The total thickness penetrated by the bullet is 8.

Explanation:

Given,

The bullet loses 25% of its momentum in penetrating a thickness of 3.5cm of the plank.

To find,

The total thickness is penetrated by the bullet.

Assume initial momentum (Pi)= mv

as the momentum exists dropped by 25 percent, the final momentum will be

$\pi -(25/100)$

$\pi Pi=(3/4)$

$\pi =Pf$

considering that the mass is constant,

pf =3/4 mv = m (3/4 v)

velocity after travelling 3.5 cm = 3/4 v

from equation v²-u²=2as

(3/4)² v²-v² = 2a (3.5)

[9/16 v² - v²] / 2(3.5) = a

Hence,

(-7/16 v²)/7 = a

We get,

a= -1/16 v²

now to discover displacement at velocity=0

0²-v² = 2 (-1/16v²) s

1= (1/8) s

s= 8 cm

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