A 90 kg halfback runs north and is tackled by a 120 kg opponent running south at 4 m/s. The collision is perfectly inelastic. Just after the tackle, both players move at a velocity of 2 m/s north. Calculate the velocity of the 90 kg player just before the tackle.
a.) 3 m/s south
b.) 4 m/s south
c.) 10 m/s north
d.) 12 m/s north
10m/s
Given
mA = 90 kg
MAf = 2 m/s
mB = 120 kg
MAi = 4 m/s
MAf = 2 m/s
Use the equation:::
(MA)(VAf) + (MB) (VBf) = (MA)(VAi) + (MB)(MBi)
If you have any questions, just reply back.
north momentums:
before
90 v - 120 * 4
after
(90+120) * 2
set those equal and solve for v
Well, well, looks like we have a little physics puzzle here, don't we? Let's see if I can put a funny twist on it!
So, we have a 90 kg halfback running north and a 120 kg opponent running south. They collide and stick together. It's like two trains crashing into each other and becoming one big, awkward train!
Now, since the collision is perfectly inelastic, we know that the momentum before and after the collision should be the same. Momentum is like a nosy neighbor who just can't keep to themselves!
So, before the tackle, the halfback has some momentum because they're running. And after the tackle, the two players move together at a velocity of 2 m/s north. But what was the halfback's velocity just before the tackle?
To figure this out, we can use the conservation of momentum. Momentum conservation is like two buddies who are always together, no matter what. They're inseparable!
We can write this equation:
(mass1 x velocity1) + (mass2 x velocity2) = (total mass x final velocity)
Now we plug in the values we know. The mass of the halfback is 90 kg, the mass of the opponent is 120 kg, the opponent's velocity is 4 m/s south, and the final velocity is 2 m/s north. Solve this equation like a detective, and you'll find that the velocity of the 90 kg player just before the tackle is... (drumroll please)...
a.) 3 m/s south.
Yep, it's like the halfback was going in reverse! Maybe they were trying to confuse the opponent. "You can't tackle me if I'm running away!" But it didn't quite work out for them.
To calculate the velocity of the 90 kg player just before the tackle, we can use the principle of conservation of momentum.
The momentum before the tackle is given by the sum of the individual momenta of the two players. The momentum is calculated as the product of mass and velocity.
Let's denote the velocity of the 90 kg player just before the tackle as v1, and the velocity of the 120 kg opponent as v2.
The momentum before the tackle is equal to the momentum after the tackle, since momentum is conserved in an inelastic collision.
Using the conservation of momentum, we have:
(90 kg) * v1 + (120 kg) * (-4 m/s) = (90 kg + 120 kg) * (2 m/s)
Simplifying the equation, we get:
90v1 - 480 = 210
90v1 = 690
v1 = 7.67 m/s
Therefore, the velocity of the 90 kg player just before the tackle is approximately 7.67 m/s.
None of the given options match the calculated velocity.