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Question from a Physics beginner

  1. Sep 29, 2005 #1
    Hi all,

    I am just beginning Physics, and have 2 simple problems but don't know how to go about solving them. Here goes:

    1) An eagle is flying due east at 8.9 m/s carrying a gopher in its talons. The gopher manages to break free at a height of 12 m. What is the magnitude of the gophers velocity as it reaches the ground?

    What formula is used to do to calculation? This is a multiple choice question, but using the Pythagorean Theorem doesn't yield any of the choices.

    The choices: 8.9 m/s, 9.8 m/s, 11 m/s 18 m/s or 22 m/s?

    2) A projectile is fired from a gun and has initial horizontal and vertical components of velocity equal to 30 m/s and 40 m/s, respectively. Determine the initial speed of the projectile.

    Again, what formula is used to do to calculation?
  2. jcsd
  3. Sep 29, 2005 #2


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    Science Advisor

    Well, of course, it wouldn't. The Pythagorean theorem doesn't have any thing to do with kinematics- and the gopher's fall will not be a straight line.
    Do you know any formulas connecting velocity and distance to time when you have a constant acceleration? Do you know what the acceleration due to gravity is?

    Exactly the same formulas you used in (1)! You should have one formula for vertical motion involving "g" (the acceleration due to gravity) and one for horizontal motion with no acceleration.
  4. Sep 29, 2005 #3
    Look at what you're asked to find here. In this case, they're asking to find the magnitude of the gopher's velocity when he hits the ground. Let's call this [tex]v_{f}[/tex]. In order to find the final velocity, [tex]v_{f}[/tex], you'll need to find the two components, [tex]v_{xf}[/tex] and [tex]v_{yf}[/tex]. These two components are related to [tex]v_{f}[/tex] by the Pythagorean theorem:

    [tex]v_{f}^2=v_{xf}^2 + v_{yf}^2[/tex]

    Now, look at what you've got. If you set the direction the eagle is flying to be +x and the direction of gravity to be +y, you can see you have [tex]v_{ix} = 8.9 m/s[/tex] given to you. You're also given that the gopher falls 12 meters, so [tex]y_{i} = 0 m[/tex] and [tex]y_{f} = 12 m[/tex]. At this point, there are 3 things you need to do to solve the equation:

    1) Find [tex]v_{xf}[/tex] from what you know about [tex]v_{xi}[/tex].
    2) Find [tex]v_{yf}[/tex] from what you know about [tex]y_{i}[/tex] and [tex]y_{f}[/tex]. This is where your kinematics equations come in.
    3) Once you've solved for [tex]v_{xf}[/tex] and [tex]v_{yf}[/tex], solve for [tex]v_{f}[/tex] using the pythagorean theorem.

    The answer I come up with is one of the choices above.

    No kinematics involved here. You're simply given the two components of the initial velocity and asked to find the initial speed, i.e., the magnitude of the initial velocity. Use the Pythogorean Theorem and solve for [tex]v_{i}[/tex] like step 3 above.
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