Question 91991: Find the time required for an object to fall to the ground form a building that is 1400 ft. high.
Found 3 solutions by stanbon, amalm06, ikleyn:
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Find the time required for an object to fall to the ground form a building that is 1400 ft. high.
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h(t) = -16t^2+1400
When it hits the ground its height is zero.
-16t^2 + 1400 = 0
16t^2 = 1400
t^2 = 1400/16
t = sqrt(1400/16)
t = 9.354... seconds
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Cheers,
Stan H.
Answer by amalm06(224)  (Show Source):
You can put this solution on YOUR website! You can solve it using energy and momentum considerations.
When the ball is at the top of the building, all of its energy is potential. At the instant before the ball touches the ground, all of its energy is kinetic. Assume the ball is in free-fall and neglect air resistance.
Therefore, 
Solve for vf: vf=sqrt(2*g*Δh)=91.45 m/s
Now use conservation of momentum. Consider a ball-Earth system, with the ball in free-fall:
FΔt=m(vf-vi)
mgΔt=mvf
Solve for Δt:
Δt=vf/g=91.45/9.8=9.33 s
The answer is correct, it's a simple application of Newtonian mechanics. Just because "Ikleyn" lacks physics knowledge does not make the answer incorrect. This is the 2nd physics problem that "Ikleyn" has gotten wrong.
Answer by ikleyn(52788)  (Show Source):
You can put this solution on YOUR website! .
1. Algebra solution
The formula for the height of a freely falling body under gravity force, that students learn and use in their Algebra exercises is
H(t) =  +  ,
where g = 32 ft/s^2 and h0 is the initial height (in feet).
In this case, h0 = 1400 ft, therefore the equation to find the time t is
H(t) = 0, or  = 0, which is equivalent to
16*t^2 = 1400, which implies t =  = 9.35 seconds.
Answer. 9.35 seconds.
2. Physics solution
In school Physics course, the students learn the formula for the distance which a freely falling body travels
vertically down under the gravity force
H(t) =  .
where the included parameters were all explained in the Algebra solution.
To find time, get from this formula t =  =  = 9.35 seconds,
and you get the same answer.
These are two standard, simplest and straightforward methods of Algebra and Physics to solve the problem.
What the tutor @amalm proposes in his post, is never used, and I do not recommend you to take it seriously.
Only the person who doesn't know basics, can propose this approach.
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