A 90kg halfback moving at 4.0m/s on an apparent breakaway for a touchdown is tackled from behind. When he was tackled by a cornerback of mass 78.3kg running at 7.48m/s in the same direction, what was their mutual speed immediately after the tackle?
how in the world do i solve this and wht is the proof for it?
(original questioner)
ok so i got
360+584.684= 90v+78.3v
945.684=168.3v
945.684/168.3=168.3v/168.3
v=5.619037... and so on.
v= 5.62 m/s?
conservation of mometum applies:
90*4+78.3*7.48=(90+78.3)V solve for V
To solve this problem, we can apply the law of conservation of momentum. According to this law, the total momentum before the collision should be equal to the total momentum after the collision.
The momentum (p) of an object is given by the product of its mass (m) and velocity (v): p = mv.
Before the tackle, the momentum of the halfback can be calculated as:
P1 = (mass of halfback) × (velocity of halfback) = 90 kg × 4.0 m/s.
The momentum of the cornerback can be calculated as:
P2 = (mass of cornerback) × (velocity of cornerback) = 78.3 kg × 7.48 m/s.
After the tackle, the halfback and the cornerback move together as a system, so their final momentum can be calculated as:
Pf = (mass of halfback + mass of cornerback) × (mutual velocity after tackle).
As per the law of conservation of momentum, P1 + P2 = Pf.
Now, let's plug in the values and solve the equation:
90 kg × 4.0 m/s + 78.3 kg × 7.48 m/s = (90 kg + 78.3 kg) × (mutual velocity after tackle).
Simplifying the equation gives:
360 kg·m/s + 584.244 kg·m/s = 168.3 kg × (mutual velocity after tackle).
944.244 kg·m/s = 168.3 kg × (mutual velocity after tackle).
Dividing both sides of the equation by 168.3 kg gives:
mutual velocity after tackle = 5.61 m/s (rounded to two decimal places).
Therefore, the mutual speed of the halfback and cornerback immediately after the tackle is 5.61 m/s.
The proof for the conservation of momentum can be found in Newton's third law of motion. According to this law, for every action, there is an equal and opposite reaction. In the case of a collision, the force exerted by the halfback on the cornerback is equal in magnitude but opposite in direction to the force exerted by the cornerback on the halfback. This exchange of forces leads to a change in momentum but keeps the total momentum of the system the same before and after the collision, thus verifying the conservation of momentum.
To solve this problem, you can apply the principle of conservation of momentum. The momentum is a vector quantity defined as the product of an object's mass and velocity. According to the principle of conservation of momentum, the total momentum before the tackle should be equal to the total momentum after the tackle.
Here's how you can calculate their mutual speed immediately after the tackle:
Step 1: Calculate the momentum of the halfback before the tackle.
Momentum of halfback = Mass of halfback * Velocity of halfback
= 90 kg * 4.0 m/s
Step 2: Calculate the momentum of the cornerback before the tackle.
Momentum of cornerback = Mass of cornerback * Velocity of cornerback
= 78.3 kg * 7.48 m/s
Step 3: Calculate the total momentum before the tackle.
Total momentum before the tackle = Momentum of halfback + Momentum of cornerback
Step 4: Apply the principle of conservation of momentum to find the mutual speed after the tackle.
Total momentum after the tackle = Total momentum before the tackle
Mutual speed = Total momentum after the tackle / (Mass of halfback + Mass of cornerback)
Now, let's perform the calculations:
Momentum of halfback = 90 kg * 4.0 m/s = 360 kg·m/s
Momentum of cornerback = 78.3 kg * 7.48 m/s = 585.444 kg·m/s
Total momentum before the tackle = 360 kg·m/s + 585.444 kg·m/s = 945.444 kg·m/s
Mutual speed = 945.444 kg·m/s / (90 kg + 78.3 kg)
Mutual speed = 945.444 kg·m/s / 168.3 kg
Mutual speed = 5.624 m/s
Therefore, their mutual speed immediately after the tackle is 5.624 m/s.
The proof for the conservation of momentum can be derived from Newton's laws of motion. The second law states that the rate of change of momentum of an object is equal to the net force acting on it. If no external forces are acting on a system, the total momentum of the system remains constant. In this case, we assume there are no external forces acting on the halfback and cornerback system, so the total momentum of the system before and after the tackle is conserved.