A 88 kg fullback moving east with a speed of 8.0 m/s is tackled by a 98 kg oppon

Question

A 88 kg fullback moving east with a speed of 8.0 m/s is tackled by a 98 kg opponent running north at 2.0 m/s. If the collision is perfectly inelastic, calculate each of the following. Hint: Since we're talking about just before the collision to just after the collision, you can use momentum conservation...but you're going to have to carefully use the fact that momentum is a vector. That means the total initial x-momentum equals the total final x-momentum and the total initial y-momemtum equals the total final y-momentum. (a) the speed of the players just after the tackle
m/s
(b) the kinetic energy lost as a result of the collision

2.82 is not supposed to be there

Explanation / Answer

P1 = m1*v1
= (88 kg)*(8 m/s)
P1 = 704

P2 = m2*v2
= (98 kg)*(2 m/s)
P2 = 196

Now for the speed, since we know the x and y components, we can calculate the magnitude of the momentum:
Ptot = sqrt[P1^2 + P2^2]
= sqrt[(704)^2 + (196)^2]
= sqrt[534032]
Ptot = 730.77

Now to plug in the momentum in the formula to find speed:
Vf = Ptot/Mtot
= 730.77/(88+98)
= 730.77/186
Vf = 3.9 m/s

b)The mechanical energy lost in the collision is equal to the total kinetic energy before the collision minus the total kinetic energy after the collsion. Remember K = 1/2 mv

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