Question

Two football players collide head-on in midair while trying to catch a thrown football. The first player is 98.5 kg and has an initial velocity of 6.05 m/s, while the second player is 119 kg and has an initial velocity of −3.50 m/s. What is their velocity (in m/s) just after impact if they cling together? (Indicate the direction with the sign of your answer.)

Answer 1

The velocity of two football players just after a head-on collision in which they cling together is 0.798 m/s. This is calculated using the law of conservation of momentum for a completely inelastic collision.

Step-by-step explanation:

The velocity of two football players just after they collide and cling together can be calculated using the law of conservation of momentum. Since they cling together after collision, it becomes a problem of a completely inelastic collision.

According to the conservation of momentum:

Initial Momentum = Final Momentum

The initial momentum is the sum of the individual momenta of the players before the collision, and the final momentum is the combined mass times the velocity just after the impact.

Initial Momentum = (mass of first player × velocity of first player) + (mass of second player × velocity of second player)

Final Momentum = (combined mass of both players) × (combined velocity after impact)

Let's calculate:

Initial Momentum = (95.0 kg × 6.00 m/s) + (115 kg × -3.50 m/s)

Initial Momentum = 570 kg·m/s - 402.5 kg·m/s = 167.5 kg·m/s

The combined mass after collision is 95.0 kg + 115 kg = 210.0 kg.

We then set the initial momentum equal to the final momentum:

167.5 kg·m/s = 210.0 kg × (combined velocity after impact)

Thus, the velocity just after impact is:

combined velocity after impact = 167.5 kg·m/s / 210.0 kg = 0.798 m/s

Answer 2

`v_f=0.825m/s`

Step-by-step explanation:

We must use conservation of linear momentum before and after the collision,
`p_i=p_f`

Before the collision we have:

`p_i=p_1+p_2=m_1v_1+m_2v_2`

where these are the masses are initial velocities of both players.

After the collision we have:

`p_f=(m_1+m_2)v_f`

since they clong together, acting as one body.

This means we have:

`m_1v_1+m_2v_2=(m_1+m_2)v_f`

Or:

`v_f=(m_1v_1+m_2v_2)/(m_1+m_2)`

Which for our values is:

`v_f=((98.5kg)(6.05m/s)+(119kg)(-3.5m/s))/((98.5kg)+(119kg))=0.825m/s`