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Kinematics pellet question

  1. Jun 13, 2007 #1
    1. The problem statement, all variables and given/known data
    A pellet is fired upward with an initial velocity of 25 m/s. At what times in the pellet 25 meters above its fired height

    2. Relevant equations
    S=ut+1/2at^2 I got it down to,
    U(initial velocity)=25 m/s
    and a=acceleration due to gravity -9.81
    I got 25=25t+1/2(-9.81)(t^2)
    then 25=25t+-4.91t^2 and I am stumped

    3. The attempt at a solution

    I tried dividing both sides by 25t, leaving
    1/t=-4.91t^2, but I really have no clue.
    I cant use the quadratic formula and I need 2 times. Any hints would be very nice! Thank you.
  2. jcsd
  3. Jun 13, 2007 #2
    I'm a little bit confused, are you not allowed to use the quadratic formula for this problem? The quadratic formula is the perfect way to solve for those two times.
  4. Jun 13, 2007 #3
    Well im in grade 10, and we haven't learned it yet, so it is off limits. Sorry for the confusion
  5. Jun 13, 2007 #4
    In that case, you should find the final velocity of this projectile motion. After you find the final velocity, you can find the times using the definition of acceleration.
  6. Jun 14, 2007 #5
    Well, let's start with what you arrived at:


    Now just factor this equation to find the values of t. You probably know the method of completing the squares, that is :

    -4.9t^2 + 25t = 25

    Dividing through whatever is multiplied on the square term

    -t^2 + (25/4.9)t = 25/4.9

    making the squared term positive

    t^2 - (25/4.9)t = -25/4.9

    Half the x coefficient (-25/4.9) -> (-25/9.8) and squaring it: (625/96.04) then adding this to both sides:

    t^2 - (25/4.9)t + 625/96.04 = -25/4.9 + 625/96.04

    then you know:

    (t - 25/9.8)^2 = (625(4.9) - 25(96.04))/(4.9)(96.04)


    (t-25/9.8)^2 = 661.5/470.596

    Thus you know that

    t - 25/9.8 = +/- sqrt (661.5/470.596)

    as both the negative and positive numbers make a square positive number.

    and thus your answers:

    t = 25/9.8 +/- sqrt (661.5/470.596)

    and using your trusty calculator you know now :

    t = 3.736627555 (for the +)
    t = 1.365413261 (for the -)
  7. Jun 14, 2007 #6
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