The equation that offers the best approximation to this result is: [tex]h = -16\cdot t^{2}+28\cdot t + 8[/tex]. (Choice D)
How to find the free fall formula for a given scenario
An object experiments a free fall when it is solely accelerated by gravity on the assumption of an uniform acceleration. The formula is described below:
[tex]h =h_{o} + v_{o}\cdot t + \frac{1}{2}\cdot g\cdot t^{2}[/tex] (1)
Where:
- [tex]h_{o}[/tex] - Initial height, in feet.
- [tex]v_{o}[/tex] - Initial speed, in feet per second.
- [tex]t[/tex] - Time, in seconds.
- [tex]g[/tex] - Gravitational acceleration, in feet per square second.
If we know that [tex]t = 2\,s[/tex], [tex]h_{o} = 8\,ft[/tex], [tex]h = 0\,ft[/tex], [tex]g = -32.174\,\frac{ft}{s^{2}}[/tex], then the height formula is:
[tex]0 = 8 +2\cdot v_{o} - \frac{1}{2}\cdot (32.174)\cdot (2)^{2}[/tex]
[tex]0 = -56.348+2\cdot v_{o}[/tex]
[tex]v_{o} = 28.174\,\frac{ft}{s}[/tex]
The equation that offers the best approximation to this result is: [tex]h = -16\cdot t^{2}+28\cdot t + 8[/tex]. (Choice D)
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