The two men, tangled together, initially sail off on the wet field at a speed of approximately 3.64 m/s.
To determine the initial speed at which the quarterback and tackle sail off on the wet field, we can use the principle of conservation of momentum.
The momentum of an object is given by the product of its mass and velocity. Since both the quarterback and the tackle are initially at rest, their initial momentum is zero. After the collision, they move together as one system.
To find their final velocity, we can set up an equation using the principle of conservation of momentum:
(mass of quarterback * velocity of quarterback) + (mass of tackle * velocity of tackle) = total momentum after collision
Given:
Mass of quarterback = 192 lb
Mass of tackle = 288 lb
Velocity of tackle = 6.1 m/s
First, let's convert the masses from pounds to kilograms:
Mass of quarterback = 192 lb * 0.4536 kg/lb = 87.09 kg
Mass of tackle = 288 lb * 0.4536 kg/lb = 130.64 kg
Now we can substitute the values into the equation:
(87.09 kg * 0 m/s) + (130.64 kg * 6.1 m/s) = total momentum after collision
0 + (130.64 kg * 6.1 m/s) = total momentum after collision
791.9844 kg⋅m/s = total momentum after collision
Since the two men move together as one system, their total momentum after the collision is also equal to their combined mass multiplied by their final velocity:
(total mass of the system) * (final velocity of the system) = 791.9844 kg⋅m/s
(total mass of the system) * (final velocity of the system) = (87.09 kg + 130.64 kg) * final velocity of the system
217.73 kg * final velocity of the system = 791.9844 kg⋅m/s
final velocity of the system = 791.9844 kg⋅m/s / 217.73 kg
final velocity of the system ≈ 3.64 m/s
Therefore, the two men, tangled together, initially sail off on the wet field at a speed of approximately 3.64 m/s.