3. Two football players interact on the field. One moving toward the right is ca

Question

3. Two football players interact on the field. One moving toward the right is carrying the ball and wants to cross the goal line. The other player moving toward the left tackles the ball carrier and holds on to the player. If the player moving toward the right has a mass of 95 kg and is moving at 3.75 m/s, and the player moving toward the left has a mass of 111 kg and is moving at 4.1 m/s,

a. What is the total momentum of the two players before they collide (vectors to the
right should be designated as positive)?

b. What is the velocity of the pair immediately after the collision?

c. Is the pair moving toward the right or the left?

d. What is the total kinetic energy of the two players before the collision in Joules?

e. What is the total kinetic energy of the two players after the collision in Joules?

Explanation / Answer

(a)This is a standard momentum problem, we that momentum is defined:
M=mv
So, for player 1:
M=95(3.75)=356.25 kgm/s
Similarly for player 2:
M=111(-4.1)=-455.1 kgm/s

(b)We know the total momentum of the system is 356.25-455.1=-98.85
Since momentum is conserved, the total momentum of the system won't change, thus:
-98.85=(95+111)v
-98.85=206v
v=-.48m/s

(c) Since the velocity that we got in the previous step was negative, they are moving left after the collision.

(d) Kinetic energy is .5mv2 so, for Player 1:
K=.5mv2
K=.5(95)(3.75)2
K=667.97J

Similarly for Player 2:
K=.5mv2
K=.5(111)(-4.1)2
K=932.96J

(e)Similarly to above but with with the combined mass and new velocity:
K=.5mv2
K=.5(206)(-.48)2
K=23.73J

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