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Collisions/Projectile Motion (AP Free-response)

  1. Jan 22, 2009 #1
    1. The problem statement, all variables and given/known data

    3. A bullet of mass m is moving horizontally with speed vowhen it hits a block with mass 100m that is at rest on a horizontal frictionless table. The surface of the table is height h above the floor. After the impact the bullet and the block slide off the table and hit the floor at a distance x from the edge of the table.

    Derive expressions in terms of m, h, Vo, and constants.

    A. The speed of the block as it leaves the table
    B. Delta KE of the system during impact
    C. The horizontal distance X.
    If the bullet passes through:
    D. Is the time to reach the floor greater, smaller or equal/ Why?
    E. Is the distance x smaller, greater equal/ Why?

    2. Relevant equations

    I'm assuming that conservation of momentum has something to do with part A; Delta KE= KEf- KEri, and KE= (0.5)mv2 for part B, General kinematics equations for Part C (I'm guessing D= Vit+0.5at2) , and I'm confused about D and E.

    3. The attempt at a solution

    A. mVo=(m+100m)Vf
    Vf=(mVo) / (m+100m) = mVo / m(1+100) = Vo/101

    B. Delta KE = KEf-KEi

    =0.5(1+100m)Vf2 - 0.5 mVo2

    C. x=Vi + 0.5at2


    I'd greatly appreciate any help/feedback.
     
  2. jcsd
  3. Jan 22, 2009 #2
    Your approaches to parts A and B are correct. Part C is not correct because there is no accelerating force in the horizontal, x, direction. So x = Vft. The time, t, is found from h = 1/2gt2 since Vo = 0 (no initial velocity in the vertical or y direction). As for parts D and E, consider if the amount of time for the block to hit the floor is independent or dependent on the initial horizontal velocity, and consider the amount of energy delivered to the block by the bullet if the bullet passed through compared to the bullet remaining in the block and how this would affect the horizontal initial velocity of the block.
     
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