Question

A bullet fired into a fixed target loses half of its velocity
after penetrating 1 cm. How much further it will penetrate
before coming to rest, assuming that it faces constant
resistance to motion
(a) 1.5 cm
(b) 1.0 cm
(c) 3.0 cm
(d) 2.0 cm​

Answer 1

Correct question :

A bullet fired into a fixed target loses half of its velocity

after penetrating 3 cm. How much further it will penetrate

before coming to rest, assuming that it faces constant

resistance to motion

Answer:

further penetrating distance = 1 cm

Step by step explanations :

Given that,

A bullet fired into a fixed target loses half of its velocity

after penetrating 3 cm.

let the its initial velocity be u

so,

after penetrating 3 cm

its velocity = u/2

Now we have,

initial velocity(u) = u

final velocity(v) = u/2

distance travelled(s) = 3 cm

v² = u² + 2as

putting the values,

(u/2)² = u² + 2a(3)

6a = u²/4 - u²

6a = -3u²/4

a = -3u²/4 × 1/6

a = -u²/8

Now,

initial velocity(u) = u/2

final velocity(v) = 0 [it will stop]

acceleration(a) = --u²/8

let the further penetrating distance be s

so,

v² = u² + 2as

0 = (u/2)² + 2(-u²/8)s

-u²s/4 + u²/4 = 0

-s/4 = -1/4

u²(-s/4 + 1) = 0

S = 1

so,

further penetrating distance = 1 cm

Answer 2

Answer: Hey mate here is your answer

Let u be initial velocity of the bullet, after penetrating 3 cm into the target the velocity reduces to u/2 .

i.e After travelling s=3 cm with initial velocity u, the final velocity v = u /2.

begin mathsize 14px style From space the space equation space of space motion comma straight v squared minus straight u squared equals 2 as straight a equals fraction numerator straight v squared minus straight u squared over denominator 2 straight s end fraction equals fraction numerator open parentheses begin display style straight u over 2 end style close parentheses squared minus straight u squared over denominator 2 cross times 3 space cm end fraction straight i. straight e. comma space straight a equals fraction numerator straight u squared minus 4 straight u squared over denominator 4 cross times 2 cross times 3 end fraction 24 space straight a equals negative 3 straight u squared straight a equals fraction numerator negative 3 straight u squared over denominator 24 end fraction equals fraction numerator negative straight u squared over denominator 8 end fraction Retardation equals straight u squared over 8 Let space apostrophe straight x apostrophe space be space the space distance space through space which space it space will space penetrate space further space and space stop. Then space straight v equals 0 comma space straight s equals straight x space and space straight u equals straight u over 2 therefore straight v squared minus straight u squared equals 2 as 0 minus open parentheses straight u over 2 close parentheses squared equals 2 cross times fraction numerator negative straight u squared over denominator 8 end fraction cross times straight x rightwards double arrow straight x equals 1 space cm end style.

Hope it's helpful for you....

Explanation: