In a ballistics test, a 26 g bullet traveling horizontally at 1000 m/s goes through a 35-cm-thick 400 kg stationary target and emerges with a speed of 950 m/s. The target is free to slide on a smooth horizontal surface.

How long is the bullet in the target?

Answer: 3.60*10^-4 s

Explanation:

Given

Mass of bullet, m = 26 g = 0.026 kg

Initial speed of bullet, u = 1000 m/s

Length of target, s = 35 cm = 0.35 m

Mass of target, M = 400 kg

Final speed of bullet, v = 950 m/s

Using equation of motion

v² = u² + 2as, making a subject of formula, we have

a = (v² - u²) / (2*s)

a = 950² - 1000² / 2 * 0.35

a = 902500 - 1000000 / 0.7

a = - 97500 / 0.7

The acceleration = - 1.39*10^5 m/s² (it is worthy of note that the acceleration is negative)

now, using another equation of motion, we have

v = u + a*t

we know our a, so we make t subject of formula

time t = (v-u) / a

t = (950 - 1000) / - 1.39*10^5

t = - 50 / - 1.39*10^5

t = 3.60*10^-4 s