In American Football a receiver has caught the ball and is now running at 9.2 m/
ID: 1398306 • Letter: I
Question
In American Football a receiver has caught the ball and is now running at 9.2 m/s parallel to the sideline, 1.0 m inbouds. A cornerback is going to try and push him out of bounds by colliding (inelastic collision) with him at 90 degrees, 3 meters before the goal line. If the receiver has a mass of 82.1 kg and the cornerback has a mass of 90.2 kg, what is the minimum velocity the cornerback needs to have as he hits the reciever to knock him out of bounds before the goal line? (Assume a classical inelastic collision)
Explanation / Answer
As it is a case of classical inelastic collision first, we must observe that Kinetic energy is not retained in the given situation, but the momentum of the two bodies is retained, so the amount of movement (momentum) is kept, therefore we can set up:
p i = pf (equation 1) where pi is the initial amount of movement and pf is the final amount of movement.
We have two moments, before and after the collision, we can name the receiver as player A and cornerback as player B. before the collision we can establish the following data:
before collision
VAi = 9.2 m/s ( initial speed of the receiver)
mAi = 82.1 Kg ( mass of the receiver)
mB i = 90.2 Kg ( mass of the cornerback)
VBi = ? (initial speed of the cornerback this is the outcome requested)
after collision
As the cornerback will hit the receiver in order to knock him out we can consider that the two players remain at rest after the collision, so the final quantity of movement will be equal to zero:
pf = 0 Kg m / s
Then we can express equation one as follows:
p i = pf (equation 1)
(mAi) (VAi ) + (mB i) (VBi ) = 0
Clearing out VBi :
VB i = -(mAi) (VAi ) / (mB i) Substituting values:
VBi = - (82.1 Kg ) ( 9.2 m/s) / (90.2 Kg) = - 8.37383592 m/s This is the requested outcome the minus sign indicates that the cornerback moves in the opposite direction to the receiver.