Answer
The mass of the car and the man is $1500~kg$
Work Step by Step
The initial momentum of the system is zero. By conservation of momentum, if the bullet gains a horizontal component of momentum $p_b$ in one direction, the car and the man will gain the same magnitude of horizontal momentum $p_c$ in the opposite direction. Since the ground exerts a normal force on the car, the car does not gain an equal and opposite vertical component of momentum.
We can find the mass $m_c$ of the car:
$p_c = p_{b,x}$
$m_c~v_c = m_b~v_{b,x}$
$m_c = \frac{m_b~v_{b,x}}{v_c}$
$m_c = \frac{(0.010~kg)(173~m/s)~cos~30.0^{\circ}}{1.0\times 10^{-3}~m/s}$
$m_c = 1500~kg$
The mass of the car and the man is $1500~kg$.
