An 87.0 kg fullback moving east with a speed of 5.0 m/s is tackled by a 83.0 kg opponent running west at 2.92 m/s, and the collision is perfectly inelastic.
Impact = m1*V1-m2*V2=87*5-83*2.92=192.6
m*V = 192.6
V = 192.6/m = 192.6/(87+83) = 1.133 m/s
Thank You So Much .
To solve this problem, we need to apply the principles of conservation of momentum and conservation of mass.
Conservation of momentum states that the total momentum before a collision is equal to the total momentum after the collision, assuming no external forces act on the system. Mathematically, this can be expressed as:
(m1 * v1) + (m2 * v2) = (m1' * v1') + (m2' * v2')
Where:
- m1 and m2 are the masses of the objects before the collision,
- v1 and v2 are the velocities of the objects before the collision,
- m1' and m2' are the masses of the objects after the collision, and
- v1' and v2' are the velocities of the objects after the collision.
In this case, the initial velocities are given as 5.0 m/s east for the fullback and 2.92 m/s west for the opponent. The masses are given as 87.0 kg for the fullback and 83.0 kg for the opponent.
Since the collision is perfectly inelastic, the two objects will stick together after the collision and move with a common final velocity.
Let's denote the final velocity of the two objects as vf. Using conservation of momentum, we can write the equation as:
(87.0 kg * 5.0 m/s) + (83.0 kg * (-2.92 m/s)) = (m1' + m2') * vf
Simplifying this equation will give us the final velocity vf.
Now, let's calculate it step by step:
Step 1: Calculate the total momentum before the collision:
m1v1 + m2v2
= (87.0 kg * 5.0 m/s) + (83.0 kg * (-2.92 m/s))
= 435 kg·m/s - 242.36 kg·m/s
= 192.64 kg·m/s (east)
Step 2: Determine the total mass after the collision:
m1' + m2'
Since the objects stick together, the masses of the fullback and the opponent add up:
m1' + m2' = 87.0 kg + 83.0 kg
= 170.0 kg
Step 3: Calculate the final velocity:
(87.0 kg * 5.0 m/s) + (83.0 kg * (-2.92 m/s)) = (170.0 kg) * vf
(435 kg·m/s - 242.36 kg·m/s) = 170.0 kg * vf
192.64 kg·m/s = 170.0 kg * vf
Now, divide both sides of the equation by 170.0 kg to solve for vf:
vf = 192.64 kg·m/s / 170.0 kg
vf ≈ 1.133 m/s (east)
Therefore, after the collision, the fullback and the opponent move in the east direction together at a speed of approximately 1.133 m/s.