Free fall question, where has my reasoning gone wrong?

  1. 1. The problem statement, all variables and given/known data
    It's a two part question, but it basically says this:

    a bolt drops from an elevator 9.0 ft from the ground, at what time does it hit the ground?

    2. Relevant equations

    x = x0 + vx0t + 1/2ax(t^2)

    3. The attempt at a solution

    since it's a free fall question and we're starting from above ground:

    0 = 9.0ft - 16ft/s^2 (t^2)

    -9.0/-16 = t^2

    t = 0.75 seconds.

    But the book says that t = 0.71 seconds..

  2. jcsd

  3. gravity is 32 ft/s^2 so 1/2ax(t^2) is -16ft/s^2(t^2)

    thanks for replying
  4. Doc Al

    Staff: Mentor

    Your answer looks fine to me.
  5. a bolt drops from an elevator 9.0 ft from the ground, at what time does it hit the ground?


    1 foot = 0.3048 m

    so 9ft = 2.7432 m

    (delta) y = Vot + 1/2(a)t^2

    so 2.7432 = 0 + 1/2(-9.80)t^2

    so 2.7432/(1/2*-9.8)=t^2

    so .5598367347 = t^2

    so t = .7482223832 or .75s
  6. how come the answer says 0.71 seconds though? the equation sqrt(9/16) is not ambiguous, since they are both perfect squares.. I can't really guess that it was a difference due to rounding can I?

  7. my math got me .75s (I stored the answers in my calculator so rounding error wouldn't be a factor)

    the book probably rounded each answer or rounded off wrong... your answer is correct
  8. DaveC426913

    DaveC426913 16,530
    Gold Member

    Yeah. I realized as soon as I posted, so I deleted it so as not to confuse.
  9. that's what I got as well, you don't need a calculator to see that the sqrt( 9 / 16) is going to be 0.75.. but the problem is that the book says 0.71s, which is strange...
  10. DaveC426913

    DaveC426913 16,530
    Gold Member

    What is the other part of this "two part question"? Is it possible that the 9.0 ft initial height was derived and thus possibly incorrect?
  11. this is the full question:

    An elevator ascends with an upward acceleration of 4.0ft/s^2. At the instant its upward speed is 8.0ft/s, a loose bolt drops from the ceiling of the elevator 9.0 ft from the floor.

    Calculate (a) the time of flight of the bolt from the ceiling to the floor

    (b) the distance it has fallen relative to the elevator shaft.

    Answer: (a) 0.71 (b) 2.3 ft

    I don't see how the other parts can affect the answer.. but there's a large chance that I'm wrong, I'm just learning physics myself through this book


    no, it is given
  12. Doc Al

    Staff: Mentor

    That's quite a bit different from the problem that you stated and solved! You can't ignore the acceleration of the elevator.
  13. hmm, but that is the acceleration going up isn't it? when it falls, wouldn't the acceleration just be gravity?

  14. DaveC426913

    DaveC426913 16,530
    Gold Member

    Yes but it's initial velocity is not zero. And the elevator floor is moving.

    This is not a two-part question. This is a one-part question that has several dependent components.
  15. Doc Al

    Staff: Mentor

    The acceleration of the bolt is just due to gravity. But you are asked for the time until it hits the moving floor, which is accelerating. You need to combine both accelerations. (Write the position of the bolt and the elevator--with respect to the ground--as functions of time. Then solve for the point at which they collide.)
  16. ohh. I thought that they meant the floor of the elevator SHAFT. thanks.

    I thought that a dropped object has an initial velocity of 0? If not, I'm not sure how I would calculate that.

    Thanks for the replies
  17. Doc Al

    Staff: Mentor

    D'oh! :wink:

    The dropped object will have the initial speed of whatever it's being dropped from. (In this case from a moving elevator.)
  18. A good way to think about this would be to think about what happens in a car. When you drop something out of the window, it keeps moving with the car's velocity, it doesn't start from rest. ;)
  19. DaveC426913

    DaveC426913 16,530
    Gold Member

    Well your equation contains a variable for initial velocity. It's just not zero.
  20. Hi, but the speed of the elevator is going from the other direction? how does the upward speed transfer to a downward speed?
  21. Doc Al

    Staff: Mentor

    What do you mean? The initial speed of the bolt when it starts to fall from the elevator is the same as that of the elevator: 8 m/s upward. (After that, gravity exerts its influence, as for any projectile.)
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