A 0.45 kg football traveling at a speed of 22 m/s is caught by an 84 kg stationary receiver. If the football comes to rest in the receiver's arms, what is the magnitude of the impulse imparted to the receiver by the ball?

The magnitude of the impulse imparted to the receiver by the football can be calculated using the principle of conservation of momentum. According to this principle, the sum of the initial momentum of the football and receiver should be equal to the sum of their final momentum.

The initial momentum of the football is given by:

pinitial = mfootball * vfootball = 0.45 kg * 22 m/s

Since the receiver is initially at rest, their initial momentum is zero:

pinitial = 0 kg * 0 m/s

Therefore, the final momentum of the receiver can be calculated as:

pfinal = mreceiver * vfinal

Since the football comes to rest in the receiver's arms, the final velocity of the receiver is zero:

pfinal = 84 kg * 0 m/s

Thus, the magnitude of the impulse imparted to the receiver is:

|pfinal - pinitial| = |mreceiver * vfinal - mfootball * vfootball|

= |84 kg * 0 m/s - 0.45 kg * 22 m/s|

= |0 - 9.9 kg m/s|

= 9.9 kg m/s

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