Two players collide in a game of boot hockey on a mostly frictionless ice surfac

Question

Two players collide in a game of boot hockey on a mostly frictionless ice surface. Before the collision, the player from the red team (with a mass of 80.0 kg) is sliding eastward, and the player from the blue team (with a mass of 50.0 kg) is sliding northward. Immediately after the collision the red player has a velocity of 6.00 m/s in a direction 37.0 degree north to east, and the blue players has a velocity of 9.00 m/s in a direction 23.0 degree south of east. (a) What was the speed of each player immediately before the collision? (b) By how much did the kinetic energy of the system (consisting of both players) change during the collision? Classify the collision as completely inelastic, inelastic, or elastic.

Explanation / Answer

Applying momentum conservation for collision:

momentum of red team + momentum of blue team before collision = momentum after collision

80 (vRi) + 50 (vB j) = 80 x 6 (cos37i + sin37j) + 50 x 9 (cos23i - sin23j)

along i direction:

80 vR = 383.34 + 414.23

vR = 9.97 m/s ............Ans (Speed of red player after collision)

along j direction:

50 vB = 113

vB = 2.26 m/s ........Ans (Speed of blue platyer after the collision)

(B) KE before the collision,

Ki = 80 x 9.97^2 / 2 + 50 x 2.26^2 / 2 = 4103.82 J

KE after collision:

Kf = 80 x 6^2 / 2 + 50 x 9^2 / 2 = 2925 J

change in KE = Kf - Ki = - 1178.8 J

So there is lost of energy hence its not elastic.

and after collision both are not moving together hence collision is not completely inelastic.

hecne collision is elastic.

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