Question

For a ballistics study, a 2.2 gm bullet is fired into soft wood. Thebullet strikes the wood surface with a velocity of 370 m/s andpenetrates 0.17 m. Find (a) the constant retarding force, N, (b)the deceleration, m/s^2, (c) the time required to stop the bullet. 

Answer 1

$m = 2.2\textsf{ gm}= 2.2×10^{-3}\textsf{ kg} \\ v = 370\textsf{ m/s}\\ d = 0.17\textsf{ m}\\$

(a)

$Fd = E_k\\ F d= 1/2mv²$

$F = \dfrac{mv²}{2d} = \dfrac{2.2×10^{-3}× 370}{2×0.17}$

$= 2.39\textsf{ N}$

(b)

$F = ma\\ 2.39 = 2.2×10^{-3}× a\\ a = 1086.5\textsf{ ms}^{-2}$

(c)

$Ft = mv²\\ 2.39×t = 2.2× 10^{-3}× (370²)\\ t = 126.02\textsf{ s}$