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If an object is dropped from a height of 141 feet, the function [tex]h(t) = -16t^2 + 141[/tex] gives the height of the object after [tex]t[/tex] seconds. When will the object hit the ground?

Answer :

The height of the object is given by:

[tex]h(t)=-16t^2+141[/tex]

to know when will it hit the ground we equate the expression to zero and solve for t:

[tex]\begin{gathered} -16t^2+141=0 \\ 16t^2=141 \\ t^2=\frac{141}{16} \\ t=\pm\sqrt[]{\frac{141}{16}} \\ t=\pm\frac{\sqrt[]{141}}{4} \end{gathered}[/tex]

Since time has to be positive it takes:

[tex]\frac{\sqrt[]{141}}{4}\text{ seconds}[/tex]

for the object to hit the ground. This is approximately 2.97 seconds.

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