Question

A bullet is fired inside a long fixed block with initial velocity vo consider motion of bullet straight line
inside the block. Retardation of bullet is f = av+b. Where a and b are constants.
VO
bullet
x=0
fixed, long block
The velocity of bullet and its position x are related as

Answer 1

Explanation:

Let, F be the thrust force .

Case (i);when the block is fixed,

v2=2mFs=2mF(3.75)

⇒2Fv2=3.75----->(a)

Case(ii): when the block is placed on a smooth plane,

in this case, thrust force gives velocity to block and decelerates bullet.

let, s1 be the distance travelled by the bullet and s2 is the distance travelled by block.

s1=v2t−211Ft2----->(1)

s2=214Ft2------------->(2)

using,

v=u+at

4Ft=v−1Ft

⇒t=5F4v

substitute above result in (1) and (2).we get,

s1=25F12v2

and s2=25F2v2

distance to which bullet penetrate=s1−s

Answer 2

Explanation:

retardation or acceleration is given by

f=vdv/dx—(1)

as given

f=av+b —(2)

now equating 1 and 2

av+b =vdv/dx

now

dx=vdv/av +b

integrating

we get

x=