Question

A 50kg football player heading to the right at 2.5 m/s

collides with and tackles a 40kg player heading left at 3.5
m/s toward him. What is the speed and direction of the
tangled players?

Answer 1

The speed of the tangled players is
`0.17\ ms^(-1)` in left direction

Step-by-step explanation:

Mass of Player 1 =
`m_1` =
`50\ kg`

Mass of Player 2 =
`m_2` =
`40\ kg`

Velocity of Player 1 moving right =
`v_1=2.5\ ms^(-1)`

Velocity of Player 2 moving left =
`v_2=-3.5\ ms^(-1)`

By law of conservation of momentum:

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

Here
`v` represents the velocity of tangled players.

Plugging in values in the equation.

`(50*2.5)+(40*(-3.5))=(50+40)v\\125-140=90v\\-15=90v\\`

Dividing both sides by 90.

`(-15)/(90)=(90v)/(90)\\-0.167=v`

∴
`v=0.167\approx 0.17\ ms^(-1)`

The negative velocity indicates that the tangled players move to the left after collision.

The speed of the tangled players is
`0.17\ ms^(-1)` in left direction