A simple ballistics test recorded that an unknown bullet entered a stationary bl

Question

A simple ballistics test recorded that an unknown bullet entered a stationary block of wood (M=1000 g) with a particular velocity that upon becoming imbedded into the block made it rise to a height of upon becoming roughly of 37 cm. Not knowing the caliber of the bullet, you have to test several bullets in order to determine what kind of bullet it was.
Determine the velocity, V, of the bullet once imbedded into the block form the following data.
Bullet A, m- 96 g, v_bullet=33.3 m/s
Bullet B, m- 105 g, v_bullet=30.2 m/s
Bullet C, m -110 g, v_bullet=27.1 m/s
Determine the height that the block rose for each bullet
Which of the three bullets is the unknown bullet mentioned in the original problem

Explanation / Answer

Momentum is conserved.

So, m1v1 = m2v2

A. (0.096 kg)(33.3 m/s) = (0.096 kg + 1 kg)(V)

==> V= 2.92 m/s

B. (0.105 kg)(30.2 m/s) = (0.105 kg + 1 kg)(V)

==> V= 2.87 m/s

C. (0.11 kg)(27.1) = (0.11 kg + 1 kg)(V)

==> V=2.69 m/s

Assuming that energy is conserved after impact with the wooden block,

1/2 · mV2 = mgh

==> 1/2 · V2 = gh

==> h = V2 / (2g)

A. (2.92 m/s)2 / (2·9.8 m/s2) = 0.435 m

B. (2.87 m/s)2 / (2·9.8 m/s2) = 0.420 m

C. (2.69 m/s)2 / (2·9.8 m/s2) = 0.369 m

So, Bullet C is the unknown bullet.

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