Two objects are moving towards each other with velocities $V_1$ and $V_2$ on a frictionless surface. They collide completely inelastically and move together after the collision with a velocity $V_3 = 17.6 \, m/s$ as shown below. If the ratio of the masses is $m_1/m_2 = 1.77$ and the angles are $\theta_1 = 38^\circ$ and $\theta_2 = 52^\circ$, what is the magnitude of $V_1$ in units of $m/s$? Express your answer using one decimal place.
