A 87 kg fullback moving east with a speed of 5.0 m/s is tackled by a 97 kg oppon

Question

A 87 kg fullback moving east with a speed of 5.0 m/s is tackled by a 97 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
J
Can you account for the missing energy? One sentence should be plenty here.

Explanation / Answer

(a)
Inital Momentum = 87*5 i^ + 97*2 j^ Kgm/s
Final Momentum = (87+97) *Vx i^ + (87 + 97) *Vy j^

Using Momentum Conservation,

Initial Momentum = Final Momentum
87*5 =  (87 +97) *Vx
Vx = 2.36 m/s

97*2 = (87 +97) *Vy
Vy = 1.05

V = sqrt(Vx^2+ Vy^2)
V = sqrt(2.36^2 + 1.05^2)
V = 2.58 m/s
Speed of the players just after the tackle, V = 2.58 m/s

(b)
Kinetic Energy Lost = Initial Kinetic Energy - Final Kinetic Energy
Kinetic Energy Lost = 0.5*87*5^2 + 0.5*97*2^2  - (87+97)*2.58^2 J
Kinetic Energy Lost = 669.1 J


Energy lost in collision is in Elastic Potential Energy.

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