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Projectile motion motorcycle jump

  1. May 20, 2016 #1
    1. The problem statement, all variables and given/known data
    The current world-record motorcycle jump is 77.0 m,
    set by Jason Renie. Assume that he left the take-off ramp at
    12.0º to the horizontal and that the take-off and landing
    heights are the same. Neglecting air drag, determine his take-off
    speed

    2. Relevant equations
    R = [(v0)^2/g]*sin2(theta)
    5 constant acceleration equations
    3. The attempt at a solution
    Hi. I understand that I can use the range equation to solve this question, but I wanted to try and use the constant acceleration equations to try and understand it a little better, however I'm getting stuck.

    Let u = the take off speed (magnitude of velocity vector)

    u_x = ucos(12)
    x_i = 0
    x_f = 77
    a_x = 0
    t = ?

    u_y = usin(12)
    a = -9.8
    y_i = 0
    y_f = 0

    I get stuck here because I don't know the time or final velocity components (not really sure how to use v_f = 0 for half the flight time either)
     
  2. jcsd
  3. May 20, 2016 #2

    PeroK

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    Science Advisor
    Homework Helper
    Gold Member

    You need to think a move or two ahead. These problems don't always come out in one step. You put ##t = ?## but you should keep going with ##t = \frac{x_f}{u \cos \theta}##

    Now, try to find a second expression for ##t## using the vertical component. You can do it either by using the time to the maximum height (where ##v_y = 0##) and symmetry of the motion. Or, you could use ##s_y = u_yt + \frac{a_y t^2}{2}## for vertical motion.
     
  4. May 20, 2016 #3
    With your help I was able to solve it! I'll try to think further ahead for future problems.

    Thanks so much!
     
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