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?

Options

A. 3.0 cm
B. 2.0 cm
C. 1.5 cm
D. 1.0 mc

Answer

D

Explanation

According to work-energy theorem,

Total work done = Change in kinetic energy
`W = Delta K`
Case I - `F xx 3 = 1/2 m ((v_0)/(2))^(2) - 1/2 m v_0^2`
Where, is resistive force and is initial speed.

Case II Let the further distance travelled by the bullet before coming to rest be s.
`:. - F (3 + s) = K_(f) - K_(i) = -1/2 mv_0^2" " implies -1/8 mv_0^2 (3 + s) = -1/2 mv_(0)^(2)`
or, `1/4 (3 + s) = 1 " or " 3/4 + s/4 = 1 " or " s = 1 cm`.