Hawk dive!

Classical Mechanics Level 1

A hawk is cruising around in the sky at around 1000 m 1000 ~m above sea level.

It spots a tasty bird flying at 100 m 100 ~m above sea level diectly below it.

If the hawk stops flying and simply dives straight down, how long should it take (in seconds) for the hawk to reach the bird?

Details and Assumptions:

  • Ignore air resistance.
  • Assume the bird doesn't move at all below the hawk.
  • Use 9.8 m s e c 2 9.8~\frac{m}{sec^2} for the acceleration due to gravity.


The answer is 13.5526.

David Stiff by David Stiff , 20, Canada

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2 solutions

David Stiff
Jun 9, 2018

Let's use the equation:

Δ x = v 0 t + 1 2 a t 2 \Delta x = v_{0}t + \frac{1}{2}at^{2}

Then we have:

900 m = ( 0 ) t + 1 2 ( 9.8 m s e c ) t 2 900~m = (0)t + \frac{1}{2}(9.8~\frac{m}{sec})t^{2}

Which simplifies to:

( 2 ) ( 900 m ) 9.8 m s e c = t 2 \dfrac{(2)(900~m)}{9.8~\frac{m}{sec}}=t^{2}

And thus:

t = 13.55 s e c t=\boxed{13.55~sec~}

3 Helpful 0 Interesting 0 Brilliant 0 Confused
Chris H
Jun 16, 2018

For objects in free fall, t = 2 h g t=\sqrt{\frac{2h}{g}} , where t = t= time, h = h= the distance of the fall, and g = g= gravitational acceleration--9.8 m/s 2 ^2 for this problem. t = 2 ( 900 ) 9.8 t=\sqrt{\frac{2(900)}{9.8}} , which simplifies to 13.553.

2 Helpful 0 Interesting 0 Brilliant 0 Confused

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