On a very muddy football field, a 110-kg linebacker tackles an 85-kg halfback. Immediately before the collision, the linebacker is slipping with a velocity of 8.8 m/s north and the half-back is sliding with a velocity of 7.2 m/s east. What is the velocity (magnitude and direction) at which the two players move together immediately after the collision?

Solution

Verified$\textbf{Givens}$

\normalsize We have the linebacker's mass is $\color{#c34632}m_A = 110kg$ and the halfback's mass is $\color{#c34632}m_B = 85kg$ .

Let $+x$-axis be east and $+y$-axis be north, so we have:

$\begin{align*} v_{A1x} & = 0 &, \qquad \qquad \qquad v_{A1y} &= 8.8\text{ m/s}\\ v_{B1x} & = 7.2\text{ m/s} &, \qquad \qquad \qquad v_{B1y} & = 0\\ \vec{\textbf{v}}_{A2} &=\ ??? &,\qquad \qquad \qquad \vec{\textbf{v}}_{B2} & = \ ??? \end{align*}$