Question

Football players A and B both have the same momentum when running downfield. Player A has a mass of 100 kg, while player B has a mass of 120 kg. Which statement below must be true?

1) Player A is running faster than player B
2) Player B is running faster than player A
3) Both players must be running with the same speed
4) Both players must have the same kinetic energy

Answer 1

Football Player A, with a mass of 100 kg, must be running faster than Football Player B, who has a mass of 120 kg, if they both have the same momentum, as momentum is the product of mass and velocity.

Step-by-step explanation:

Momentum and Speed of Football Players

If football players A and B have the same momentum while running downfield but have different masses, we must determine which player is running faster. Since momentum is the product of mass and velocity, we can infer that if Player A has a mass of 100 kg and Player B has a mass of 120 kg, for them to have the same momentum, Player A must be running at a higher speed than Player B. This is in accordance with the formula for momentum, which is:

p = m × v

Therefore, if they both have the same momentum and Player A has a lesser mass, the only way to balance the equation is if Player A has a greater velocity. So, the statement that must be true is:

1) Player A is running faster than Player B.

This is because for momentum to be conserved across different masses, the object with the smaller mass must have a greater velocity.

Regarding kinetic energy, which is given by the formula KE = 1/2 m v^2, since the speeds of the players differ if their momenta are the same, their kinetic energies would not be equal.