Two football players collide head-on in midair while chasing a pass. The first player has a 100 kg mass and an initial velocity of 4.00 m/s in the positive x direction, while the second player has a 130 kg mass and initial velocity of
3.30 m/s
in the negative x direction. What is the x component of their velocity just after impact if they cling together? (Indicate the direction with the sign of your answer.)
I can't figure it out
To find the x component of their velocity just after impact, we can use the principle of conservation of momentum. According to this principle, the total momentum before the collision should be equal to the total momentum after the collision.
The equation for momentum is given by:
p = m * v
Where:
- p is the momentum
- m is the mass
- v is the velocity
Before the collision, the momentum of the first player can be calculated as:
p1 = m1 * v1
= (100 kg) * (4.00 m/s)
= 400 kg·m/s
Similarly, the momentum of the second player is:
p2 = m2 * v2
= (130 kg) * (-3.30 m/s)
= -429 kg·m/s
Since the players cling together after the collision, their final total momentum is:
pf = p1 + p2
= 400 kg·m/s + (-429 kg·m/s)
= -29 kg·m/s
The total mass after the collision is the sum of the individual masses:
m_total = m1 + m2
= 100 kg + 130 kg
= 230 kg
Finally, we can find the x component of the velocity after impact by dividing the total momentum by the total mass:
v_f = pf / m_total
= (-29 kg·m/s) / 230 kg
≈ -0.126 m/s
Therefore, the x component of their velocity just after impact is approximately -0.126 m/s in the negative x direction.