A 110-kg tackler moving at 2.5m/s meets head-on (and holds on to) an 82-kg halfback moving at 5.0m/s. What will be their mutual speed immediately after the collision?
Given: M1 = 110kg, V1 = 2.5m/s.
M2 = 82kg, V2 = -5m/s(left).
M1*V1+M2*V2 = M*1*V+M2*V
110*2.5+82*(-5) = 110V+82V
275-410 = 192V
-135 = 192V
V = -0.70m/s(left).
To determine the mutual speed of the tackler and the halfback after the collision, we can apply the principle of conservation of momentum.
The momentum of an object is defined as the product of its mass and velocity. The principle of conservation of momentum states that when two objects collide and there are no external forces acting on them, the total momentum before the collision is equal to the total momentum after the collision.
Let's calculate the momentum of the tackler and the halfback before the collision.
The momentum of an object can be calculated using the formula:
Momentum = mass x velocity
The momentum of the tackler before the collision is:
Momentum (tackler) = mass (tackler) x velocity (tackler)
= 110 kg x 2.5 m/s
= 275 kg·m/s
The momentum of the halfback before the collision is:
Momentum (halfback) = mass (halfback) x velocity (halfback)
= 82 kg x 5.0 m/s
= 410 kg·m/s
Now, we can apply the principle of conservation of momentum to find the mutual speed after the collision.
According to the principle of conservation of momentum:
Total momentum before the collision = Total momentum after the collision
Therefore:
Momentum (tackler) + Momentum (halfback) = Total momentum after the collision
275 kg·m/s + 410 kg·m/s = Total momentum after the collision
Total momentum after the collision = 685 kg·m/s
Now, let's determine the mutual speed after the collision using the formula for momentum:
Momentum = mass x velocity
685 kg·m/s = (mass of tackler + mass of halfback) x velocity (mutual)
Since the tackler holds on to the halfback after the collision, their masses combine:
Total mass = mass (tackler) + mass (halfback)
= 110 kg + 82 kg
= 192 kg
Rearranging the equation and solving for velocity (mutual):
velocity (mutual) = Momentum / Total mass
= 685 kg·m/s / 192 kg
≈ 3.57 m/s
Therefore, the mutual speed of the tackler and the halfback immediately after the collision is approximately 3.57 m/s (rounded to two decimal places).
To find the mutual speed of the tackler and halfback immediately after the collision, we can apply the law of conservation of momentum.
The law of conservation of momentum states that the total momentum of a system remains constant if there are no external forces acting on it.
In this case, the system consists of the tackler and halfback. Before the collision, the total momentum of the system is given by the sum of the individual momenta:
Total momentum before = (mass of tackler × velocity of tackler) + (mass of halfback × velocity of halfback)
Total momentum before = (110 kg × 2.5 m/s) + (82 kg × 5.0 m/s)
Next, we need to determine the total mass of the system. We can calculate it by adding the masses of the tackler and the halfback:
Total mass = mass of tackler + mass of halfback
Total mass = 110 kg + 82 kg
Once we have the total mass of the system and the total momentum before the collision, we can use the conservation of momentum to find the mutual speed after the collision.
According to the conservation of momentum:
Total momentum before = Total momentum after
(mass of tackler × velocity of tackler) + (mass of halfback × velocity of halfback) = Total mass × mutual speed
Plugging in the values we calculated earlier:
(110 kg × 2.5 m/s) + (82 kg × 5.0 m/s) = (110 kg + 82 kg) × mutual speed
Now, we can solve for the mutual speed after the collision:
(275 kg·m/s) + (410 kg·m/s) = (192 kg) × mutual speed
685 kg·m/s = 192 kg × mutual speed
mutual speed = 685 kg·m/s / 192 kg
mutual speed ≈ 3.57 m/s
Therefore, the mutual speed of the tackler and halfback immediately after the collision will be approximately 3.57 m/s.
conserve momentum --
110*2.5 + 0*82(-5) = (110+82)v
Now solve for v