On a touchdown attempt, a 95.0 kg running back runs toward the end zone at 3.75 m/s. A 111 kg linebacker moving at 4.10 m/s meets the runner in a head-on collision. If the two players stick together, what is their velocity immediately after the collision?

Question

Adrian Ayala · Accepted Answer

#v=0.480 m.s^(-1)# in the direction that the linebacker was moving in.

The collision is inelastic as they stick together. Momentum is conserved, kinetic energy is not. Work out the initial momentum, which will be equal to the final momentum and use that to solve for the final velocity. Initial momentum. Linebacker and runner are moving in opposite directions… choose a positive direction. I will take the direction of the linebacker as positive (he has larger mass and velocity, but you can take the runner's direction as positive if you want, just be consistent). Terms : #p_i#, total initial momentum; #p_l#, linebacker's momentum; #p_r#, runner's momentum. #p_i = p_l + p_r = 111 × 4.10 + 95.0 × (-3.75) = 455.1 - 356.25 = 98.85 kg.m.s^(-1)# That is, #98.85 kg.m.s^(-1)# in the direction of the linebacker because the value is positive. Apply conservation of momentum. Total final momentum, #p_f = p_i#. Runner and linebacker "stick" together, so their masses combine. After the collision there is only one object moving (i.e. linebacker + runner). So now : #p_f = m_(l+r) × v_(l+r) ⇒ v_(l+r) = p_f / m_(l+r)# #v_(l+r)= 98.85 / (111+ 95) = 0.480 m.s^(-1)# The velocity is positive indicating that the two move in the direction that the linebacker was moving in.

Parker Abbott · Answer

undefined To find the velocity of the combined mass after the collision, you can use the principle of conservation of momentum. The total momentum before the collision equals the total momentum after the collision.

Total momentum before collision = Total momentum after collision

(mass of running back * velocity of running back) + (mass of linebacker * velocity of linebacker) = (mass of combined players * velocity of combined players)

(95 kg * 3.75 m/s) + (111 kg * 4.10 m/s) = (95 kg + 111 kg) * velocity of combined players

(356.25 kg*m/s) + (455.1 kg*m/s) = (206 kg) * velocity of combined players

811.35 kg*m/s = (206 kg) * velocity of combined players

velocity of combined players = 811.35 kg*m/s / 206 kg

velocity of combined players ≈ 3.93 m/s