in one of msu\'s seven sacks, msu linebacker denicos allen sacked um quarterback

Question

in one of msu's seven sacks, msu linebacker denicos allen sacked um quarterback devin gardner. just prior to being sacked, the quarterback was at rest. just after they collided, the two players were momentarily stuck together and both slide a distance of 1.5 m before coming to a stop. in addition, assume this motion was purely horizontal. denicos allen's mass was 103.3 kg and devin gardner's mass was 92.8 kg.

a.the acceleration of the two players due to the frictional force is 2.45 m/s2. what was the magnitude of the velocity of the two players immediately after their collision?

b.what was the total impulse delivered to the two players during their slide?

c. what was the magnitude of the velocity of denicos allen just before he sacked the quarterback?

Explanation / Answer

Third Equation of motion

v^2 = u^2 + 2 * a * s

v = 0 (Since coming to rest)

s = 1.5 m

a = -2.45 m/s^2

0 = u^2 + 2 * (-2.45) * 1.5

u^2 = 7.35

u = 2.711 m/s

a) Velocity of two player immediately after their collision = 2.711 m/s

Impulse = change in momentum

Impulse = (m1 + m2)v - (m1 + m2)u

m1 = 103.3 kg

m2 = 92.8 kg

Impulse = 0 - (103.3 + 92.8) * 2.711

b) total impulse delivered to the two players during their slide = -531.62 Ns

By Conservation of momentum

m1 * v1 + m2 * v2 = (m1 + m2)u

103.3 * v1 + 0 = 531.62

v1 = 5.146 m/s

c) magnitude of the velocity of denicos allen just before he sacked the quarterback = 5.146 m/s

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