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1 August, 15:40

Charlotte, a 60.0-kg skin diver, shoots a 2.0-kg spear with a speed of 15 m/s at a fish who darts quickly away without getting hit. How fast does Charlotte move backwards when the spear is shot? (Hint: To start, Charlotte and the spear are together and both are at rest)

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  1. 1 August, 17:45
    0
    Charlotte move backwards with 0.5 m/s when the spear is shot

    Explanation:

    Before collision;

    m₁ = 60 kg

    m₂ = 2 kg

    v = 0 (since, Charlotte and the spear are together and both are at rest)

    After collision

    m₁ = 60 kg

    m₂ = 2kg

    v₁ = ?

    v₂ = 15 m/s

    From principle of conservation of linear moment, total momentum before collision must be equal to total momentum after collision.

    v (m₁ + m₂) = m₁v₁ + m₂v₂

    0 (60+2) = 60v₁ + 2 x 15

    0 = 60v₁ + 30

    60v₁ = - 30

    v₁ = - 30/60

    v₁ = - 0.5 m/s

    Therefore, Charlotte move backwards with 0.5 m/s when the spear is shot.
  2. 1 August, 18:51
    0
    0.5 m/s

    Explanation:

    From Newton's third law of motion,

    Total momentum before collision = Total momentum after collision

    mu+m'u' = mv+m'v' ... Equation 1

    Where m = mass of the Charlotte, m' = mass of the spear, u = initial velocity of the Charlotte, u' = initial velocity of the spear, v = Final velocity of the Charlotte, v' = Final velocity of the spear.

    Note: Since the Charlotte and the spear where initially at rest,

    0 = mv+m'v'

    -mv = m'v'

    make v the subject of the equation

    v = - (m'v'/m) ... Equation 2

    Given: m = 60 kg, m' = 2.0 kg, v' = 15 m/s

    Substitute into equation 2

    v = - (2*15/60)

    v = - 0.5 m/s.

    The negative sign shows that the Charlotte moves backward, which is in opposite direction to the motion of the spear
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