Question

Two football players with mass 75kg and 100kg run directly toward each other with speeds of 6 m/s and 8 m/s respectively, If they grab each other as they collide, the combined speed of the two players just after the collision would be:

Answer 1

Answer:

2 m/s

Explanation:

From the law of conservation of momentum,

Total momentum before collision = total momentum after collision

mu+m'u' = V(m+m') .................................Equation 1

Where m = mass of the first player, u = initial speed of the first player, m' = mass of the second player, u' = initial speed of the second player, V = combined speed of both players.

Making V the subject of the equation,

V = (mu+m'u')/(m+m')................ Equation 2

Note: Taking the direction of the first player as positive.

Given: m = 75 kg, m' = 100 kg, u = 6 m/s, u' = -8 m/s (opposite the first player),

Substituting into equation 2

V = [(75×6)+(100×(--8))]/(75+100)

V = (450-800)/175

V = 350/175

V = - 2 m/s.

Note: The negative signs tells that the combined speed is in the direction of the second player.

Hence the combined speed of the two players = 2 m/s