A 111 kg linebacker running at 1.9 m/s and a 82 kg quarterback running at 3 m/s have a head-on collision in midair. The linebacker grabs and holds onto the quarterback. (a) What is their combined speed immediately after the collision

Explanation:

mass of linebacker, m = 111 kg

initial velocity, u = 1.9 m/s

mass of quarterback, m' = 82 kg

initial velocity, u' = 3 m/s

(a) Let they are moving in the same direction, the velocity is v after collision.

Use conservation of momentum

m u + m' u' = (m + m') v

111 x 1.9 + 82 x 3 = (111 + 82) v

v = 2.4 m/s

Let they are moving in opposite direction, the velocity is v after collision.

Use conservation of momentum

m u - m' u' = (m + m') v

111 x 1.9 - 82 x 3 = (111 + 82) v

v = - 0.18 m/s