A 75 kg linebacker moving at 6 m/s is running towards an 80 kg tackle moving at 4 m/s. If they collide and stick together, how fast will they be moving after the collision?
After the collision, the combined mass of the two players is 155 kg and they will be moving at a velocity of 4.8 m/s.
To determine the final velocity of the linebacker and tackle after the collision, 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 momentum of an object is calculated by multiplying its mass by its velocity (momentum = mass × velocity). Therefore, we can calculate the initial momentum of the linebacker and tackle separately.
The initial momentum of the linebacker can be calculated as follows:
Momentum of the linebacker = mass × velocity
= 75 kg × 6 m/s
= 450 kg·m/s
Similarly, the initial momentum of the tackle can be calculated as:
Momentum of the tackle = mass × velocity
= 80 kg × 4 m/s
= 320 kg·m/s
Since the linebacker and tackle stick together after the collision, their combined mass will be the sum of their individual masses (75 kg + 80 kg = 155 kg). Let's denote the final velocity of the combined mass as V.
Now, using the principle of conservation of momentum, we can equate the total initial momentum to the total final momentum:
Initial momentum of linebacker + Initial momentum of tackle = Final momentum of combined mass
450 kg·m/s + 320 kg·m/s = 155 kg × V
770 kg·m/s = 155 kg × V
To find V, we divide both sides of the equation by 155 kg:
V = 770 kg·m/s ÷ 155 kg
V = 4.968 m/s (rounded to three decimal places)
Therefore, after the collision, the linebacker and tackle will be moving together at a speed of approximately 4.968 m/s.
To solve this problem, we can apply the principle of conservation of momentum. In an isolated system, the total momentum before and after the collision remains constant.
The momentum (p) of an object is defined as the product of its mass (m) and velocity (v), represented as p = m * v.
Before the collision, the momentum of the linebacker can be calculated as follows:
Momentum of linebacker before collision = mass of linebacker * velocity of linebacker
= 75 kg * 6 m/s
= 450 kg·m/s
Similarly, the momentum of the tackle before the collision is:
Momentum of tackle before collision = mass of tackle * velocity of tackle
= 80 kg * 4 m/s
= 320 kg·m/s
Since the linebacker and tackle stick together after the collision, their combined mass is 75 kg + 80 kg = 155 kg.
The total momentum after the collision is the sum of their individual momenta before the collision.
Total momentum after collision = 450 kg·m/s + 320 kg·m/s
= 770 kg·m/s
To find the final velocity (v_f) of the combined linebacker and tackle, we can use the equation p = m * v.
Total momentum after collision = total mass * final velocity
770 kg·m/s = 155 kg * v_f
Dividing both sides of the equation by 155 kg:
v_f = 770 kg·m/s / 155 kg
v_f ≈ 4.97 m/s
Therefore, after the collision, the combined linebacker and tackle will be moving at approximately 4.97 m/s.