Question

A bullet of mass 50 g is moving with a velocity of 500 m s^-1. It penetrated 10 cm into a still target and comes to rest. Calculate:

1. the kinetic energy possessed by the bullet, and
2. the average retarding force offered by the target.

Answer 1

(a) Mass of bullet = 50g = `50/1000 = 1/20 kg`

Velocity = 500 m/s

∴ K.E. of bullet = `1/2 mv^2`

= `1/2 xx 1/20 xx 500 xx 500`

K.E. = 6250 J

(b) u = 500 m/s,  v = 0 as bullet comes to rest
distance covered = 10 cm = `10/100 = 1/10 m`

v² - u² = 2aS

0 - 500 × 500 = `2a × 1/10`

∴ a = - 1250000 m/s^-2

∴ Retardation = 1250000 m/s^-2

But F = m × a

∴ Retarding force offered by target = `1/20 xx 1250000`

F = 62500 N