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A pine cone is 40 feet above the ground when it falls from a tree. The height h in feet of the pine cone above the ground can be modelled by h=-16t^2+40, where t is the time in seconds since the pine cone started to fall. Solve the equation for t. Write your answer in simplest form.

Answer :

Answer:

Step-by-step explanation:

Given

height of the pine cone above the ground can be modelled by

[tex]h=-16t^2+40[/tex]

When pine cone reaches the ground [tex]h=0[/tex]

[tex]\Rightarrow 0=-16t^2+40[/tex]

[tex]\Rightarrow 40=16t^2[/tex]

[tex]\Rightarrow t=\sqrt{\frac{40}{16}}[/tex]

[tex]\Rightarrow t=\frac{\sqrt{40}}{4}[/tex]

[tex]\Rightarrow t=\frac{2\sqrt{10}}{4}[/tex]

[tex]\Rightarrow t=\frac{\sqrt{10}}{2}[/tex]

[tex]\Rightarrow t=1.58\ s[/tex]

Thus cone take 1.58 s to reach ground

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