Question

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

Answer 1

@Diwakar .... i never get de concept.... my heads achin thinkin abt dis

Answer 2

"losses half velocity after entering before coming to rest" ?
Can u please write the complete question? What u want to find?

Answer 3

oopz srry...

Answer 4

do u know abt work energy thm?
there are two ways of solving this problem! It is a bit easier through W.E thm.

Answer 5

i'm nt sure cn u tell me....

Answer 6

wait a minute, i will type both the methods.

Answer 7

oh, don't worry. It is the one and the same method.I am typing it now

Answer 8

We first need to find acceleration of the bullet.
We are given that its speed decreases from v to v/2 after travelling s=3cm

We know that v^2-u^2 =2as ................................(1)
Here v=final velocity = v/2
u =initial velocity =v
s=3cm
We can find a = -3v^2 / 8s

Now we want to find the distance s' that it will further travel so that it stops. We will again use the eqn (1) but this time we will be finding s instead of a which we know already from above.

Now we have,
v=0
u=v/2
a=-3v^2/8s
s=s'

After putting in the eqn (1)
s'=-v^2/4a

Put the value of a and you will find that v^2 cancels and you will find s' in terms of s which you know to be 3cm.