How to work. a 78 kg defensive back moving 8.5 m/s tackles a 72 kg receiver moving at 7.5 m/s. what is the post-collision speed immediately after the tackle? show work

Hiya! This depends on what angle they are approaching each other before they collided.The two simple cases are if they are running in the same direction or opposite direction from each other. For either case, use the conservation of momentum equation to solve: M_total*V_result = M1*V1 + M2*V2

Here are two possible solutions.

Head-on collision: M1=78, V1=8.5, M2=72, V2=-7.5 (that's negative because he's running the other way), M_total = 78+72 = 150, so V_result = (78*8.5 - 72*7.5)/150 = 0.82 m/s. Sanity check, they weigh about the same and so most of their velocity should cancel out.

Running the same way: change the sign of V2 to positive so V_result = (78*8.5 + 72*7.5)/150 = 8.02 m/s. Sanity check, they weigh about the same and the resultant speed is between the two starting velocities.