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20 September, 22:25

6. A. 25 kg arrow with a velocity of 12 m/s to the west strikes and pierces the center of a 6.8 kg target. a. What is the final velocity of the combined mass? b. What is the decrease in kinetic energy during the collision?

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  1. 21 September, 01:29
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    (a) the final velocity of the combined mass is 9.43 m/s

    (b) the decrease in kinetic energy during the collision is 386.1 J

    Explanation:

    Given;

    mass of arrow, m₁ = 25 kg

    initial velocity of arrow, u₁ = 12 m/s

    mass of target, m₂ = 6.8 kg

    initial velocity of the target, u₂ = 0

    Part (a)

    From the principle of conservation of linear momentum;

    Total momentum before collision = Total momentum after collision

    m₁u₁ + m₂u₂ = v (m₁+m₂)

    where;

    v is the final velocity of the combined mass

    25 x 12 + 0 = v (25 + 6.8)

    300 = v (31.8)

    v = 300/31.8

    v = 9.43 m/s

    Part (b)

    Kinetic Energy, K. E = ¹/₂mv²

    Initial kinetic energy = ¹/₂m₁u₁² + ¹/₂m₂u₂² = ¹/₂ x 25 x (12) ² + 0 = 1800 J

    Final kinetic energy = ¹/₂m₁v² + ¹/₂m₂v² = ¹/₂v² (m₁ + m₂)

    = ¹/₂ x (9.43) ² (25+6.8)

    = 1413.91 J

    Decrease in kinetic energy = Initial K. E - Final K. E

    Decrease in kinetic energy = 1800J - 1413.91 J = 386.1 J
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