A bullet is fired into a tree trunk (Figure 1.12), striking it with an ini- tial velocity of 350 m/ s. If the bullet penetrates the tree trunk to a depth of 8.0 cm and comes to rest, what is the acceleration of the bullet?

Answer 1

To find the acceleration of the bullet, we need to use the kinematic equation:

v² = u² + 2as

Where:
v = final velocity (0 m/s since the bullet comes to rest)
u = initial velocity (350 m/s)
a = acceleration (unknown)
s = displacement (8.0 cm = 0.08 m)

Substituting the given values into the equation:

0² = (350 m/s)² + 2a(0.08 m)

0 = 122500 m²/s² + 0.16a

Rearranging the equation:

0.16a = -122500 m²/s²

Dividing both sides by 0.16:

a = -(122500 m²/s²) / 0.16

a ≈ -765,625 m²/s²

Therefore, the acceleration of the bullet is approximately -765,625 m²/s².