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Constant V and A problem

  1. Jan 28, 2014 #1
    1. The problem statement, all variables and given/known data

    You are driving at a constant speed on a straight highway that passes under an overpass. At time , when your car is a distance from the overpass, a prankster on the overpass releases a water balloon from rest from a height above the highway below.

    Answer the following questions. You should treat the car as a point particle, ignoring its height, length, and width.

    (a) Suppose that you don’t see the water balloon until it explodes on your windshield. At what speed were you originally traveling, given that the water balloon strikes your car? Express your answer in terms of d, h, and any relevant constants. Simplify your answer as much as possible.

    (b) Now suppose that you see the prankster release the water balloon at t=0 , and you slam on your brakes at time in an attempt to avoid being hit. (Your reaction time is Tb>0 .) Your car slows down with a constant acceleration of magnitude . The balloon hits the highway right in front of your car at the instant your car comes to rest. At what speed Vo were you originally traveling, given that the water balloon just barely misses your car? Express your answer in terms of d,h As,Tb and any relevant constants. Simplify your answer as much as possible.

    (c) Let Va be the speed you found in part (a), and let Vb be the speed you found in part (b). Which of these two speeds is larger? Justify your answer mathematically, with comments as necessary.


    2. Relevant equations

    x=vt
    v=at
    x=at^2



    3. The attempt at a solution

    Acceleration of balloon= 9.8m/s^2 or -g.

    So ballon time to hit ground is t=sqrt(h/-g)

    d= distance car travels to hit the balloon

    d=Vo sqrt(h/-g) therefore Vo = d/(sqrt(h/-g))

    For part b I am not sure how to account for the reaction time.

    Thanks
     
  2. jcsd
  3. Jan 28, 2014 #2

    haruspex

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    That's not quite right, and has led you to a wrong answer.
    Just develop some equations. Let the speed be v0. How far will you travel during your reaction time? How much further while braking?
     
  4. Jan 30, 2014 #3
    corrections

    I have made some corrections to my work and would like to know if I am correct.

    I used the formula x-x naught= Vnaught t +1/2at^2

    Balloons accelration= g
    Height= h
    Velocity of car=Vnaught

    The Vnaught of the ballon is zero.

    So I said

    h=Vnaugh t +1/2 gt^2 therefore t = sqrt(2h/g)= Time the balloon takes to fall.

    The car must travel (d) on the time the balloon takes to fall (t).
    The time the car traveled would be d/Vnaught
    So I plugged d/Vnaught into h=1/2 gt^2

    This led me to calculate that Vnaught= d sqrt(g/2h)

    Is this correct?


    For part B I let t=sqrt(2h/g)= time the balloon takes to fall

    As= deceleration of the car
    Tb= the reaction time.

    The distance the car moves is the overall distance minus the velocity initial times the braking time.

    so d=(d-Vnaught Tb)

    The final velocity of the car (V) is zero.

    so I said d=Vnaught sqrt(2h/g)+1/2 (As) 2h/g.......correct or not?
     
  5. Jan 30, 2014 #4

    haruspex

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    Good.
    Please avoid using labels generically. The speeds of the car and balloon are different, so give them different names.
    Yes
    Again, label the two distances differently.
    I can't be certain because I don't know which version of d this is, but it could be.
     
  6. Jan 30, 2014 #5
    That version of d is the distance the car moves minus the initial velocity times the braking time d=(d-Vnaught Tb) Therefore am I correct?

    Thanks
     
  7. Jan 30, 2014 #6

    haruspex

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    Yes (but you mean reaction time; braking time is the time during braking).
     
  8. Jan 30, 2014 #7

    akh

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    Why is the time used in the last equation t rather than (t-tb)?
     
  9. Jan 30, 2014 #8

    haruspex

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    Good catch, thanks. :redface:
     
  10. Jan 30, 2014 #9
    c) Let Va be the speed you found in part (a), and let Vb be the speed you found in part (b). Which of these two speeds is larger? Justify your answer mathematically, with comments as necessary.

    For Va I have Va=dsqrt(g/2h)

    For Vb I have Vb=(dg-Ash)/(g(2sqrt(2h/g)-tsub b))

    How can I determine which is larger? Can a kinematic equation by applied?

    Thanks
     
  11. Jan 31, 2014 #10

    haruspex

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    That doesn't look right. Please show your working to that point, preferably using clearer notation. Try using subscripts, sqrt symbol, etc.
     
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