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A hailstone falls from a cloud at a height of 1,600 ft. If the equation for height as a function of time is h(t) = -16t2 + initial height where t is time in seconds and h(t) is height in feet, how many seconds will it take for the hailstone to hit the ground? [?] seconds ​

Respuesta :

boffeemadrid

Answer:

10 seconds

Step-by-step explanation:

The function is

[tex]h(t)=-16t^2+\text{Initial height}[/tex]

Initial height = 1600 ft

t = Time taken

[tex]0=-16t^2+1600[/tex]

[tex]\Rightarrow -16t^2=-1600[/tex]

[tex]\Rightarrow t^2=\dfrac{1600}{16}[/tex]

[tex]\Rightarrow t^2=100\\\Rightarrow t=\pm 10[/tex]

So, time taken by the hailstone to reach the ground is [tex]10\ \text{seconds}[/tex].

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