Answer
The mass of the bullet is $2.54\times10^{-3}kg$
Work Step by Step
The arrangement of the bullets is in the figure below. 2 bullets with mass $m=4.5\times10^{-3}kg$ fly at velocity $v=324m/s$. The other bullet with mass $M$ flies at velocity $V=575m/s$. After colliding with one another, they all stop, meaning $\sum p_f=0$
We take a look at the y-component of the motions.
- 2 bullets with mass $m$ have $v_y=+324\cos60=+162m/s$
- The other bullet has $V_y=-575m/s$
From conservation of momentum, we have $$2mv_y+MV_y=\sum p_{fy}=0$$ $$M=\frac{2mv_y}{-V_y}=2.54\times10^{-3}kg$$
