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 4.5m/s, grabs him. The tackler holds onto the receiver, and and the two move off together with a velocity of 2.6m/s. The mass of the tackler is 115kg. Assuming that momentum is conserved, find the mass of the receiver.

conservation of momentum applies

Momentum tackler= momentumbothafter
115*4.5=(115+M)2.6

84.04kg

Well, well, well, looks like the receiver got himself in quite a situation, huh? A tackler running at 4.5m/s with a mass of 115kg? That's like a runaway refrigerator coming at you!

Now, according to the mighty law of momentum conservation, the initial momentum of the tackler is equal to the final momentum of the tackler and the receiver combined. So let's do some math magic, shall we?

The initial momentum of the tackler is given by:
Momentum = mass × velocity
Momentum = 115kg × 4.5m/s

Now, for the final momentum of the tackler and the receiver combined, we have:
Momentum = (mass of tackler + mass of receiver) × velocity of both

Since we know the initial and final momentum must be equal, we can set up an equation:

115kg × 4.5m/s = (115kg + mass of receiver) × 2.6m/s

Now, let's solve this riddle and find the mass of the receiver. Brace yourselves, here comes the fun part!

115kg × 4.5m/s = (115kg + mass of receiver) × 2.6m/s

518.25kg·m/s = (115kg + mass of receiver) × 2.6m/s

518.25kg·m/s ÷ 2.6m/s = 115kg + mass of receiver

199.326923076923kg = 115kg + mass of receiver

mass of receiver = 199.326923076923kg - 115kg

mass of receiver = 84.326923076923kg

And there you have it, folks! The mass of the receiver is approximately 84.33kg. The tackler might need some extra muscles to bring him down now!

To solve this problem, we can make use of the principle of conservation of linear momentum. The total momentum before the tackler grabs the receiver is equal to the total momentum after they move off together.

Linear momentum is given by the equation:

𝑝 = 𝑚𝑣

Where 𝑝 is momentum, 𝑚 is mass, and 𝑣 is velocity.

Let's consider the momentum before they move off together. The receiver is standing still, which means his velocity is zero. Therefore, the momentum of the receiver before being grabbed is zero:

𝑝_𝑟𝑒𝑐𝑒𝑖𝑣𝑒𝑟_𝑏𝑒𝑓𝑜𝑟𝑒 = 𝑚_𝑟𝑒𝑐𝑒𝑖𝑣𝑒𝑟 * 𝑣_𝑟𝑒𝑐𝑒𝑖𝑣𝑒𝑟_𝑏𝑒𝑓𝑜𝑟𝑒
𝑝_𝑟𝑒𝑐𝑒𝑖𝑣𝑒𝑟_𝑏𝑒𝑓𝑜𝑟𝑒 = 𝑚_𝑟𝑒𝑐𝑒𝑖𝑣𝑒𝑟 * 0
𝑝_𝑟𝑒𝑐𝑒𝑖𝑣𝑒𝑟_𝑏𝑒𝑓𝑜𝑟𝑒 = 0

Now, let's consider the momentum after they move off together. The velocity of the tackler is given as 2.6 m/s. We are also given the mass of the tackler as 115 kg. Let 𝑚_𝑟𝑒𝑐𝑒𝑖𝑣𝑒𝑟 be the mass of the receiver that we need to find.

𝑝_𝑡𝑎𝑐𝑘𝑙𝑒𝑟_𝑎𝑓𝑡𝑒𝑟 = 𝑚_𝑡𝑎𝑐𝑘𝑙𝑒𝑟 * 𝑣_𝑡𝑎𝑐𝑘𝑙𝑒𝑟_𝑎𝑓𝑡𝑒𝑟
𝑝_𝑡𝑎𝑐𝑘𝑙𝑒𝑟_𝑎𝑓𝑡𝑒𝑟 = 115 kg * 2.6 m/s

Since the total momentum is conserved, we can equate the two momenta:

𝑝_𝑟𝑒𝑐𝑒𝑖𝑣𝑒𝑟_𝑏𝑒𝑓𝑜𝑟𝑒 = 𝑝_𝑡𝑎𝑐𝑘𝑙𝑒𝑟_𝑎𝑓𝑡𝑒𝑟
0 = 115 kg * 2.6 m/s

Solving for 𝑚_𝑟𝑒𝑐𝑒𝑖𝑣𝑒𝑟, we have:

𝑚_𝑟𝑒𝑐𝑒𝑖𝑣𝑒𝑟 = (0) / (2.6 m/s)
𝑚_𝑟𝑒𝑐𝑒𝑖𝑣𝑒𝑟 = 0 kg

Therefore, the mass of the receiver is 0 kg, indicating a calculation mistake or a conceptual error in the problem statement. It is not possible to determine the mass of the receiver based on the given information.

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