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Projectile Launched at an Angle: Velocity

  1. Oct 24, 2015 #1
    1. The problem statement, all variables and given/known data
    A bridge rises 321 m above the water. Supposed Jack kicks the rock horizontally off the bridge. The magnitude of the rock's horizontal displacement is 45.0 m. Find the speed at which the rock was kicked.

    2. Relevant equations
    Kinematics I think?
    v = vo + at
    Δx = vot + 0.5at2
    v2 = vo2 + 2aΔx

    3. The attempt at a solution
    Well, to start off I tried to divide it into x and y components:

    x direction
    vo = ?
    v = ?
    Δx = 45
    a = 0
    t = ? t found: 8.09 sec

    y direction
    vo = 0
    v = ?
    Δx = 321 m
    a = 9.8 m/s2
    t = ? t found: 8.09 sec

    So then I tried finding t (which would be the same for both):
    321= 0.5(9.8)t2
    t = 8.09

    But what to do know? What would be the initial velocity of the rock?
    Please help, thanks everyone!
     
  2. jcsd
  3. Oct 25, 2015 #2

    SteamKing

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    You were given how far the rock traveled in the x-direction after it was kicked. You calculated the time it took for the rock to fall from the bridge and hit the ground below.

    What else do you need to calculate the speed of the rock when it was kicked?
     
  4. Oct 25, 2015 #3
    You need to apply this equation to both the vertical and the horizontal directions.

    In the vertical direction we have

    ##\Delta y=v_{oy}t+\frac{1}{2}a_yt^2##.

    And in the horizontal direction we have

    ##\Delta x=v_{ox}t+\frac{1}{2}a_xt^2##.

    Can you show how this follows from the equation for the vertical displacement?

    Then you use the value of ##t## you got using this equation in the equation for the horizontal displacement.
     
  5. Oct 25, 2015 #4
    OK, and what would be the initial velocity after that? :confused:
     
  6. Oct 25, 2015 #5
    Would I have to find the square root of the two velocity scalars added together?
     
  7. Oct 25, 2015 #6
    Or would the initial velocity be the initial velocity of the x component?
     
  8. Oct 25, 2015 #7
    You have initial vertical velocity, its acceleration and distance traveled. The rock will travel forward until it is stopped by the water.
     
  9. Oct 25, 2015 #8
    Thanks for all the replies :).
    So how would I use all this information to get the overall initial velocity? Is there some kind of formula or would I have to calculate it in some other way?
     
  10. Oct 25, 2015 #9

    SteamKing

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    Well, the rock is launched horizontally off the bridge, according to the problem statement.

    You've done all the heavy lifting in this problem. All that remains is to calculate the horizontal velocity.
     
  11. Oct 25, 2015 #10
    Ohh so the horizontal initial velocity is the answer to the problem?
     
  12. Oct 25, 2015 #11

    SteamKing

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    Well, sometimes the most important part of solving a problem isn't making all the fancy calculations. It's reading and understanding what the problem wants.

    When in doubt, re-read the problem statement.
     
  13. Oct 25, 2015 #12
    OK :)
    TY all :woot:!
     
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