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13 June, 11:12

A 50 gram bullet is fired through a 5 kg block of wood resting on a frictionless surface. The bullet has an initial speed of 500 m/s, while the block is initially at rest. After passing through the block, the bullet has a speed of 300 m/s. How fast is the wooden block moving after the bullet passes through it?

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  1. 13 June, 11:27
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    v₂ = 2 m/s

    Explanation:

    Given that

    m₁ = 50 gm, u₁ = 500 m/s, v₁ = 300 m/s

    m₂ = 5 kg, u₂=0

    The final speed of the block = v₂

    There is no any external force in the system that is why the linear momentum of the system will be conserved

    Initial linear momentum = Final linear momentum

    m₁u₁ + m₂ u₂ = m₁v₁+m₂ v₂

    0.05 x 500 + 5 x 0 = 0.05 x 300 + 5 x v₂

    25 + 0 = 15 + 5 v₂

    25 - 15 = 5 v₂

    10 = 5 v₂

    v₂ = 2 m/s

    So the final speed of the wooden block will be 2 m/s.
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