Projectile motion (No initial velocity or time)

  1. This is the problem:
    Let's ignore the second part, because I can't even get to there yet (sounds simple enough if I figured out the first part).

    What I am stuck on, is the fact I have no initial velocity or time. So I have two unknowns.
    Here is what I think I know. The acceleration is 9.8 m/s^2 due to gravity. Since I have the same y position, at the highest point P, where the velocity is 0, it should be exactly in the middle? So 100m.
    If I use, 100m as x when y is at it's highest, I can turn that into a right angle. And do: (100)*tan 45 degrees = 100m. So the height at point P is 100m.

    I'm assuming these are the only equations I am suppose to use:
    v= v(i) + at
    x = x(i) + v(i)t + 1/2at^2
    v^2 = v(i)^2 + 2a(x-x(i))

    x=100m
    y=100m
    t=?
    v(i)=?
    a=9.8 m/s^2

    and also for y, since they are independent. And I think x and y have the same answer in this case, because they both have the same magnitude (at least cut in half). However, it doesn't look like I can solve for anything in any of the equations.

    What should I be doing next?
     
  2. jcsd
  3. Basically for question 1 you need to have separate the information into a vertical component and a horizontal component.
    Vertical: u=?, v=0, a=-9.8 and x=100, as you calculated. From here use equation v^2=(u^2)+2as, where u=initial velocity and s=displacement. From this you schould get u=44.3m/s.
    Now Horizontal: velocity is always constant horizontally so u=v and a=0. So use the formula s=ut+0.5a(t^2) and substitute values and transpose to get t. You should end up with t=4.51 secs.
     
  4. tony873004

    tony873004 1,555
    Science Advisor
    Gold Member

    In your example, wouldn't u=44.3 be the total initial velocity. Then he'd need to extract the x-component for the next step giving a final time in the 6 to 7 second range?
     
  5. Too true tony, i forgot to breakdown the u=44.3 into a horizontal component. Once broken down it should equal 31.32m/s and this correct value for u leads to t=6.38m/s. Sorry guys
     
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