In a football game, a receiver is standing still, having just caught a pass. Before he can move, a tackler, running at a velocity of +3.62 m/s, grabs him. The tackler holds onto the receiver, and the two move off together with a velocity of +1.66 m/s. The mass of the tackler is 84.6 kg. Assuming that momentum is conserved, find the mass of the receiver

Question

In a football game, a receiver is standing still, having just caught a pass. Before he can move, a tackler, running at a velocity of +3.62 m/s, grabs him. The tackler holds onto the receiver, and the two move off together with a velocity of +1.66 m/s. The mass of the tackler is 84.6 kg. Assuming that momentum is conserved, find the mass of the receiver

Answer 1

To find the mass of the receiver, we can use the principle of conservation of momentum. The total momentum before the tackle is equal to the total momentum after the tackle.

Let's denote the mass of the receiver as "mr" (unknown) and the initial velocity of the receiver as "vr" (which is 0 since he's standing still). The mass of the tackler is given as 84.6 kg, and his initial velocity is +3.62 m/s.

The total initial momentum (before the tackle) is calculated as the product of the mass and velocity of each object, so it is:
Initial momentum = (mass of receiver * velocity of receiver) + (mass of tackler * velocity of tackler)

Since the receiver is standing still, his initial velocity is 0:
Initial momentum = (mr * 0) + (84.6 kg * 3.62 m/s)
Initial momentum = 0 + 306.792 kg m/s
Initial momentum = 306.792 kg m/s

After the tackle, the receiver and the tackler move together with a velocity of +1.66 m/s. The total final momentum (after the tackle) is again calculated as the product of the mass and velocity of each object, so it is:
Final momentum = (mass of receiver * velocity of receiver) + (mass of tackler * velocity of tackler)

Since they move together, their final velocity is the same:
Final momentum = (mr * 1.66 m/s) + (84.6 kg * 1.66 m/s)
Final momentum = 1.66(mr + 84.6) kg m/s

According to conservation of momentum, the initial momentum should be equal to the final momentum:
Initial momentum = Final momentum
306.792 kg m/s = 1.66(mr + 84.6) kg m/s

Simplifying the equation:
306.792 = 1.66mr + 140.196

Rearranging the equation to solve for "mr":
1.66mr = 306.792 - 140.196
1.66mr = 166.596
mr = 166.596 / 1.66
mr = 100.36 kg

Therefore, the mass of the receiver is approximately 100.36 kg.

;oin

To find the mass of the receiver, we can use the principle of conservation of momentum. The total momentum before the tackle is equal to the total momentum after the tackle.