Answer
The speed of the car before the collision was 19.5 m/s.
The speed of the truck before the collision was 21.9 m/s.
Work Step by Step
Let $v_c$ be the initial speed of the car.
$m_c~v_c = p_x$
$m_c~v_c = (m_c+m_t)~v_f~sin(\theta)$
$v_c = \frac{(m_c+m_t)~v_f~sin(\theta)}{m_c}$
$v_c = \frac{(950~kg+1900~kg)(16.0~m/s)~sin(24.0^{\circ})}{950~kg}$
$v_c = 19.5~m/s$
The speed of the car before the collision was 19.5 m/s.
Let $v_t$ be the initial speed of the truck.
$m_t~v_t = p_y$
$m_t~v_t = (m_c+m_t)~v_f~cos(\theta)$
$v_t = \frac{(m_c+m_t)~v_f~cos(\theta)}{m_t}$
$v_t = \frac{(950~kg+1900~kg)(16.0~m/s)~cos(24.0^{\circ})}{1900~kg}$
$v_t = 21.9~m/s$
The speed of the truck before the collision was 21.9 m/s.
