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24 October, 22:26

A hot air balloon is rising upward with a constant speed of 2.50m/s. When the balloon is 3.0 m above the ground, the balloonist drops a compass over the side of the balloon. How much time elapses before the compass hits the ground?

PS. Do you mind explaining why you chose a certain formula or why you plugged in certain values?

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Answers (2)
  1. 24 October, 22:34
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    Let's assume that the balloonist dropped the compass over the the side as the balloon still rising upward at 2.5m/s

    So you have:

    Vi = - 2.5 m/s (because the compass is still going with the balloon as it starts to fall down)

    d = 3 m

    a = 9.81 m/s^2

    At first you use this formula to find the Vf (finally velocity):

    Vf^2 = Vi^2 + 2ad

    Vf^2 = 6.25 + 2 (9.81) (3)

    Vf^2 = 65.11

    Vf = 8.07 m/s

    Finally you use this formula to find the time:

    Vf = Vi + at

    8.07 = - 2.5 + (9.81) t

    10.57 = (9.81) t

    t = 1.08 s

    Your final answer is 1.07 seconds.
  2. 24 October, 23:57
    0
    In the first answer submitted, Samuel got a good answer. But for the life of me,

    I'm having trouble following his solution. I'm not that great at math and physics,

    so here's how I did it:

    I always call 'up' positive and 'down' negative, and I use one single

    formula for the height of anything that's tossed or dropped:

    H = Height at any time

    H₀ = height when it's released = 3m

    V₀ = vertical speed when it's released = 2.5 m/s

    T = time after it's released

    G = acceleration of gravity = - 9.8 m/s²

    H = H₀ + V₀T - 1/2 G T²

    H = 3 + 2.5T - 4.9T²

    That's the height of the compass at any time after it's dropped, and

    we simply want to know the time ' T ' when H = 0 (it hits the ground).

    - 4.9T² + 2.5 T + 3 = 0

    That's a perfectly good quadratic equation, which you can solve for ' T '.

    The solutions are T = - 0.567sec and T = 1.078sec.

    The one with physical significance in the real situation is T = 1.078sec.
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