Question

A 98-kg fullback is running along at 8.6 m / s when a 76-kg defensive back running in the same direction at 9.8 m / s jumps on his back. What is the post-collision speed of the two players immediately after the tackle

Answer 1

The question requires calculating the post-collision speed of two football players using the law of conservation of momentum. The initial momenta of the players are summed up and then divided by their combined mass to find the final velocity after collision, using the formula: initial momentum = (combined mass) * final velocity.

Step-by-step explanation:

The subject of this question involves applying the conservation of momentum to find the post-collision speed of two football players. To solve the problem, we use the principle that in an isolated system (without external forces), the total momentum before the collision is equal to the total momentum after the collision. The formula for momentum is p = mv, where m is the mass and v is the velocity. For two objects colliding and moving together:

Given:

- Mass of fullback, m1 = 98 kg

- Velocity of fullback, v1 = 8.6 m/s

- Mass of defensive back, m2 = 76 kg

- Velocity of defensive back, v2 = 9.8 m/s

We calculate the total initial momentum:

initial momentum = (m1 * v1) + (m2 * v2)

Now, because after the collision they move together as one object, their combined mass is (m1 + m2), and let's call their final velocity vf. The conservation of momentum tells us that:

initial momentum = (m1 + m2) * vf

Therefore, we can solve for vf as follows:

vf = initial momentum / (m1 + m2)

By plugging in the given values, we can compute the post-collision speed of the two players immediately after the tackle.

Answer 2

The total momentum before and after the collision must be conserved.

The total momentum before the collision is:

`p_i = m_1 v_1 + m_2 v_2`
where m1 and m2 are the masses of the two players, and
`v_1` and
`v_2` their initial velocities. Both are considered with positive sign, because the two players are running toward the same direction.

The final momentum is instead

`p_f = (m_1+m_2)v_f`
because now the two players are moving together with a total mass of (m1+m2) and final speed vf.

By requiring that the momentum is conserved

`p_i=p_f`
we can calculate vf, the post-collision speed:

`m_1 v_1 + m_2 v_2 = (m_1+m_2)v_f`

`v_f = (m_1 v_1 + m_2 v_2)/(m_1 +m_2)= ((98 kg)(8.6 m/s)+(76 kg)(9.8m/s))/(98 kg+76 kg)=9.1 m/s`
and the direction is the same as the direction of the players before the collision.