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Projectile motion, please check my work

  1. Sep 26, 2008 #1
    1. The problem statement, all variables and given/known data
    A bird is flying horizontally at a constant velocity of 2 m/s. 10 meters under the bird, there is a man that wants to shoot the bird. He is holding his gun at an angle of 45 degrees from horizontal. The initial velocity of the bullet is 25 m/s. When the man must open fire?


    2. Relevant equations
    x = x.init + x.velocity.init * time + 0.5 * accel.x * time^2
    y = y.init + y.velocity.init * time + 0.5 * accel.y * time^2
    time=t

    3. The attempt at a solution

    First, I find the x and y components of the initial velocity of the bullet:
    x.velocity.init.bullet = 25 * cos(45 degrees) = 17.68 m/s
    y.velocity.init.bullet = 25* sin(45 degrees) = 17.68 m/s

    Then, since the bird always stays at a height of 10 meters, I find how much time the bullet takes to reach this height.
    y = y.init + y.velocity.init * time + 0.5 * accel.y * time^2
    10 = 0 + 17.68*t + 0.5*-9.8*t^2
    t = 0.702 s

    I find the horizontal position of the bullet after 0.702 seconds
    x = 17.68m/s * 0.702 s
    x = 12.41 m

    Now, I find how much time the bird takes to fly 12.41 meters
    x = initial x + x.velocity.bird * time
    12.41 = 0 + 2*t
    t = 6.205 s

    The final answer is 6.205-0.702 = 5.503 seconds

    Is my work correct?
    Sorry for my bad english.
     
  2. jcsd
  3. Sep 26, 2008 #2

    gabbagabbahey

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    Gold Member

    It looks pretty good to me: I get t= 5.51s which means that the hunter must shoot 5.51s after the bird is over top of him, or in terms of distance, when the bird is 11.01m away from him.
     
    Last edited: Sep 26, 2008
  4. Sep 26, 2008 #3
    Work looks alright to me, but I just skimmed over it quickly.
     
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