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24 September, 15:13

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:

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  1. 24 September, 15:31
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    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
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