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

Question

A bullet fired into a fixed target loses half its velocity after penetrating 3 cm . How much further it will penetrate before coming to rest assuming that it faces constant resistance to motion? (A) 1.5cm (B) 1.0 cm (C) 3.0 cm (D) 2.0 cm

Tardigrade Admin · Accepted Answer

For first part of penetration, by equation of motion, ((u/2)=(u-2 f(3). or 3 u2=24 f For latter part of penetration, 0=((u/2))2-2 f x or u2=8 f x Therefore, 3 ×(8 f x)=24 f or x=1 cm

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

$1.5 c m$

$1.0 c m$

$3.0 c m$

$2.0 c m$

For first part of penetration, by equation of motion,
$(\frac{u}{2} = (u - 2 f (3)$
or $3 u^{2} = 24 f$
For latter part of penetration,
$0 = (\frac{u}{2})^{2} - 2 f x$
or $u^{2} = 8 f x$
Therefore,
$3 \times (8 f x) = 24 f$
or $x = 1 c m$

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

1.5cm

1.0cm

3.0cm

2.0cm