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Tricky Motion Problem

  1. Sep 3, 2007 #1
    1. The problem statement, all variables and given/known data

    A daredevil decides to jump a canyon. Its walls are equally high and 10 m apart. He takes off by driving a motorcycle up a short ramp sloped at an angle of 15 degrees. What minimum speed must he have in order to clear the canyon?



    2. Relevant equations


    v = v(initial) + at
    Distance = (vi)(t) + 1/2a(t^2)
    v^2= v(initial)^2 + 2(a)(distance)


    3. The attempt at a solution

    I am completely stumped on this one... All I know is that

    Vox = v cos(15)
    Voy = v sin(15)
     
  2. jcsd
  3. Sep 4, 2007 #2
    Have a look around HyperPhysics under mechanics>velocity and acceleration>trajectories you can look at Range of Trajectory for an equation to use. as well as how they got it.

    Sorry if you're not supposed to use that but that's all I could find ^.^ you can probably do it using vectors and x=x0+v0*t+.5*a*t^2
     
  4. Sep 4, 2007 #3

    cristo

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    Ok, that's a good start-- you've noticed that you need to split the motion up into horizontal and vertical components. Now, note the other information you know; the acceleration in the vertical direction, the displacement in the horizontal direction when the vehicle lands, the displacement in the vertical direction when the vehicle lands. So, we have the following information:
    ay=-g; ax=0
    x=10; y=0.

    Now, you can apply your second equation to the vertical direction (the y direction) to find an expression for t. Once you have t, you can apply the second equation again in the horizontal direction to find v0. Have a go, and post your attempts.
     
  5. Sep 4, 2007 #4
    I hope i have understood the question right.

    Remember that his range should be 10m+length of bike.You havent given lenght of bike so its a problem but if the length hasnt been given itself in the question then its safe to assume range to be 10m.So u can get Vo from the formula for range.

    Means Vo^2*Sin2@/g = r.
    So (Vo^2*1/2)/10 = 10 =>> Vo^2=200 =>> Vo = 10*2^1/2 that is 10 root 2.

    where i have taken g = 10,Vo = initial velocity,@=angle of projection and r = range.
     
  6. Sep 4, 2007 #5

    cristo

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    To use the kinematic equations we model objects as particles, and so the length of the motorcycle is not required (if you include the length of the bike, where do you measure the distance from? the front, the back, the middle? ..)

    I also find it more useful for a student to refrain from using such equations like the range equation. Not only does it mean memorising fewer equations, but it also means a student is more capable of handling different questions by manipulation of the four kinematic equations.
     
  7. Sep 4, 2007 #6
    We measure the distance the instant its front part flies in air till its back part reaches the ground.I have done a few questions like this.Well anyway if in the question if it hasnt been given its of no use.

    ON the second part.Its completely true what u said.NEVER USE FORMULA BLINDLY but since i knew how this question had to be done I quickly used the Range equation which is automatically memorised since I have used it extensively.
     
  8. Sep 5, 2007 #7
    I am trying it, but I am lost, all these sin and cos functions are killing me... any clues?
     
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