Question

A bullet fired into a fixed target loses half of its velocity after penetrating 3cm. How much further it will penetrate before coming to rest assuming that it faces constant resistance motion.

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Answer 1

Answer:

it will penetrate before coming to rest

= 1 cm

Step by step explanations :

given that,

A bullet fired into a fixed target loses half of its velocity after penetrating 3cm

let initial velocity of the bullet be u

since

final velocity is half of initial velocity

so,

final velocity = u/2

distance travelled in this situation

= 3 cm

now we have,

initial velocity(u) = u

final velocity(v) = u/2

distance travelled(s) = 3 cm

by the equation of motion,

v² = u² + 2as

(u/2)² = u² + 2a(3)

6a + u² = u²/4

6a = u²/4 - u²

6a = -3u²

a = -u²/8

a = -u²/8

now,

initial velocity(u) = u/2

final velocity(v) = 0 cm/s

[bullet will stop]

a = -u²/8

v² = u² + 2as

(0)² = (u/2)² + 2(-u²/8)s

0 = u²/4 - 2u²s/8

u²/4 - u²s/4 = 0

(u² - u²S)/4 = 0

u² - u²S = 0

u²(1 - S) = 0

1 - S = 0

-s = -1

S = 1 cm

so,

it will penetrate before coming to rest

= 1 cm