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 +4.9 m/s, grabs him. The tackler holds onto the receiver, and the two move off together with a velocity of +3.4 m/s. The mass of the tackler is 125 kg. Assuming that momentum is conserved, find the mass of the receiver.

conservation of momentum

125*4.9= (125+M)3.4

solve for M

m= 55.14 kg

To solve this problem, we can use the principle of conservation of momentum. According to this principle, the total momentum before the tackler grabs the receiver should be equal to the total momentum after they move off together.

Let's assign variables to the given information:
- Velocity of the tackler before grabbing the receiver (v1) = +4.9 m/s
- Combined velocity of the tackler and receiver after they move off together (v2) = +3.4 m/s

The momentum (p) of an object is calculated by multiplying its mass (m) by its velocity (v). Therefore, we have the following equations:

Total momentum before = Total momentum after
(mass of tackler * velocity of tackler before) = (mass of tackler * velocity of tackler and receiver after) + (mass of receiver * velocity of receiver after)

Mathematically, this can be written as:
(mass of tackler * v1) = (mass of tackler * v2) + (mass of receiver * v2)

Now we can solve for the mass of the receiver.

Let's plug in the given values:
125 kg * 4.9 m/s = 125 kg * 3.4 m/s + mass of receiver * 3.4 m/s

To isolate the mass of the receiver, we can rearrange the equation:
mass of receiver * 3.4 m/s = 125 kg * 4.9 m/s - 125 kg * 3.4 m/s

Simplifying:
mass of receiver * 3.4 m/s = 612.5 kg*m/s - 425 kg*m/s
mass of receiver * 3.4 m/s = 187.5 kg*m/s

Now, divide both sides of the equation by 3.4 m/s to solve for the mass of the receiver:
mass of receiver = 187.5 kg*m/s / 3.4 m/s
mass of receiver ≈ 55.15 kg

Therefore, the mass of the receiver is approximately 55.15 kg.

To find the mass of the receiver, we can use the conservation of momentum principle, which states that the total momentum before an event is equal to the total momentum after the event.

In this case, before the tackler grabs the receiver, the receiver is standing still, so his initial velocity is 0 m/s. The tackler is moving at +4.9 m/s.

Let's assign variables to the unknowns:
- Mass of the receiver = m (to be determined)
- Mass of the tackler = 125 kg
- Initial velocity of the tackler = +4.9 m/s
- Final velocity of both the receiver and the tackler = +3.4 m/s

According to the conservation of momentum, the total momentum before the tackler grabs the receiver is equal to the total momentum after they move off together.

Before the tackler grabs the receiver, the total momentum is the momentum of the tackler:
Momentum before = (mass of the tackler) * (initial velocity of the tackler)
= (125 kg) * (+4.9 m/s)

After the tackler grabs the receiver and they move off together, the total momentum is the combined momentum of both the receiver and the tackler:
Momentum after = (mass of the receiver + mass of the tackler) * (final velocity of both)

Since momentum is conserved, we can equate the two equations:
(mass of the tackler) * (initial velocity of the tackler) = (mass of the receiver + mass of the tackler) * (final velocity of both)

Substituting the given values:
(125 kg) * (+4.9 m/s) = (m + 125 kg) * (+3.4 m/s)

Now we can solve for the mass of the receiver (m):

125 kg * 4.9 m/s = (m + 125 kg) * 3.4 m/s
612.5 kg * m/s = (m + 125 kg) * 3.4 m/s
612.5 kg = 3.4 m/s * m + 3.4 m/s * 125 kg
612.5 kg - 3.4 m/s * 125 kg = 3.4 m/s * m
612.5 kg - 425 kg = 3.4 m/s * m
187.5 kg = 3.4 m/s * m
m = 187.5 kg ÷ 3.4 m/s

Therefore, the mass of the receiver is approximately 55.15 kg.