Problem 8-75 Inelastic collision - Part 6

Two trucks have a completely inelastic collision. After the collision, they have a common velocity of \(11 \;m/s\) at \(35^\circ\) south of west. Before the collision, one truck \((\text{mass} \; 2.3\times10^4\; kg)\) has a velocity of \(15\; m/s\) at \(51^\circ\) south of west. Determine the initial velocity (magnitude and direction) of the other truck \((\text{mass} \; 1.2\times10^4\; kg).\)

Accumulated Solution

FBD with illustration of before and after

\(v_{1x} = (-15) \cos 51 \\ v_{2x} = v_2 \cos \theta \\ v_x{'} = (-11) \cos 35 \\ m_1v_{1x} + m_2v_{2x} = (m_1 + m_2)v_x{'} \\ v_{2x} = -8.2\; m/s\)

\((2.3 \times 10^4\; kg)(-15) \cos 51 + (1.2 \times 10^4\; kg)v_{2x} = (3.5x \times 10^4\; kg)(-11) \cos 35 \\ v_{2x} = -8.2 \;m/s\)

Which are the \(y\) components of the velocities?

Solution \(v_{1x}\) \(v_{2x}\) \(v_x{'}\)
(A) \((-15) \cos 51\) \(v_2 \cos \theta \) \((-11) \cos 35\)
(B) \((-15) \sin 51\) \(v_2 \sin \theta\) \((-11) \sin 35\)
(C) \((15) \cos 51\) \(v_2 \cos \theta\) \((11) \cos 35\)
(D) \((15) \sin 51\) \(v_2 \sin \theta\) \((11) \sin 35\)