A football player of mass 103 kg running with a velocity of 2.0 m/s [E] collides head-on with a 110 kg player on the opposing team travelling with a velocity of 3.2 m/s [W]. Immediately after the collision the two players move in the same direction. Calculate the final velocity of the two players.

M1*V1 + M2*V2 = M1*V + M2*V.

103*2 + 110*(-3.2) = 103V + 110V,
V = -0.685 m/s. = 0.685 m/s West.

Well, calculating velocities after a collision can be quite a handful, but lucky for you, I'm here to clown around and make it fun!

So, we have a football physics extravaganza happening here! Two players, one collision, and a whole lot of momentum to calculate. Let's get started, shall we?

Since the players are moving in opposite directions before the collision, we can say that they have opposite velocities. The first player has a mass of 103 kg and a velocity of 2.0 m/s [E], while the second player weighs in at 110 kg and has a velocity of 3.2 m/s [W].

To solve this, we'll need to figure out the total momentum before and after the collision and then apply the principle of conservation of momentum. According to this principle, the total momentum of a system remains constant before and after any interaction or collision.

The total momentum before the collision can be calculated by taking the sum of the individual momenta of the players, which is the product of their respective masses and velocities. We can call this value P1.

For the first player:
P1 = (mass1 x velocity1) = (103 kg x 2.0 m/s) = 206 kg·m/s [E]

For the second player:
P2 = (mass2 x velocity2) = (110 kg x -3.2 m/s) = -352 kg·m/s [W] (negative because they're going in the opposite direction)

Now, let's look at the total momentum after the collision, which we can call P3. Since the players move in the same direction after the collision, we need to add their individual momenta:

P3 = (mass1 x velocity1') + (mass2 x velocity2')

We need to find the new velocities, denoted by velocity1' and velocity2'. Let's assume that velocity1' is the final velocity of the first player, and velocity2' is the final velocity of the second player.

Now, here comes the magic part! We can use the principle of conservation of momentum to equate P1 and P3:

P1 = P3

206 kg·m/s [E] = (mass1 x velocity1') + (mass2 x velocity2')

Substituting the given mass values, we get:

206 kg·m/s [E] = (103 kg x velocity1') + (110 kg x velocity2')

Now, luckily for us, we have one more important piece of information – the players move in the same direction after the collision. This means their velocities should have the same sign after the collision.

Let's add up their masses since they are moving in the same direction:

(103 kg + 110 kg) = 213 kg

Substitute this value into our equation:

206 kg·m/s [E] = (213 kg x velocity')

Solving for velocity', we find:

velocity' = 206 kg·m/s [E] / 213 kg
velocity' ≈ 0.968 m/s [E] (rounded to three decimal places)

So, after all that momentum calculation and clowning around, the final velocity of both players is approximately 0.968 m/s [E]. That's quite the collision, isn't it?

I hope that clears things up for you! Keep those football physics questions coming, and I'll keep serving up the laughs!

To solve this problem, we can use the principle of conservation of momentum. According to this principle, the total momentum before the collision is equal to the total momentum after the collision.

The momentum of an object is calculated by multiplying its mass by its velocity. Let's denote the initial velocity of the first player as v1i, the initial velocity of the second player as v2i, the final velocity of both players as vf, and the mass of the first player as m1 and the mass of the second player as m2.

According to the conservation of momentum principle, we can write the following equation:

(m1 * v1i) + (m2 * v2i) = (m1 * vf) + (m2 * vf)

Let's substitute the given values into the equation:

(103 kg * 2.0 m/s) + (110 kg * -3.2 m/s) = (103 kg + 110 kg) * vf

Simplifying the equation further:

206 kg*m/s - 352 kg*m/s = 213 kg * vf

-146 kg*m/s = 213 kg * vf

Now, we can solve for vf by dividing both sides of the equation by 213 kg:

vf = (-146 kg*m/s) / 213 kg
vf ≈ -0.686 m/s

The negative sign indicates that both players are moving in the opposite direction of their initial velocities.

Therefore, the final velocity of both players after the collision is approximately -0.686 m/s.

To solve this problem, we can use the principle of conservation of momentum. According to this principle, the total momentum of a system remains constant before and after a collision, as long as no external forces are acting on the system.

The momentum (p) of an object is calculated by multiplying its mass (m) by its velocity (v). Mathematically, this can be represented as:

p = m * v

Let's first calculate the initial momentum of each player:

Player 1 (football player):
Mass (m1) = 103 kg
Velocity (v1) = 2.0 m/s [E]

p1 = m1 * v1

Player 2 (opposing player):
Mass (m2) = 110 kg
Velocity (v2) = 3.2 m/s [W]

p2 = m2 * v2

Since the two players collide head-on, the velocity of player 1 changes from east to west, while the velocity of player 2 changes from west to east. To account for the directions, we can assign negative signs to the velocities:

Player 1: v1 = -2.0 m/s [E]
Player 2: v2 = 3.2 m/s [W]

Now, let's calculate the initial momenta:

p1 = m1 * v1 = 103 kg * (-2.0 m/s) = -206 kg m/s
p2 = m2 * v2 = 110 kg * 3.2 m/s = 352 kg m/s

The total initial momentum of the system can be obtained by adding the individual momenta:

Initial momentum (before the collision) = p1 + p2 = -206 kg m/s + 352 kg m/s = 146 kg m/s

Since momentum is conserved, the total momentum of the system after the collision will also be 146 kg m/s. Now, let's assume that the final velocity of both players is v (in the same direction).

p1' = m1 * v
p2' = m2 * v

We can now express the conservation of momentum as follows:

p1' + p2' = p1 + p2

m1 * v + m2 * v = -206 kg m/s + 352 kg m/s

Calculating the sum of the masses:

103 kg * v + 110 kg * v = 146 kg m/s

Simplifying the equation:

213 kg * v = 146 kg m/s

Finally, solving for v:

v = 146 kg m/s / 213 kg

v ≈ 0.686 m/s

Therefore, the final velocity of both players after the collision is approximately 0.686 m/s in the same direction as before the collision.