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An object is dropped from a height of 100 meters. The function below models the relationship between t , the number of seconds after the object is dropped, and f(t) , the height of the object after it is dropped. f(t)=100−4.9t^2 Approximately how many seconds does it take for the object to hit the ground?

Respuesta :

MrRoyal

Answer:

[tex]t = 4.52[/tex]

Step-by-step explanation:

Given

[tex]f(t) = 100-4.9t^2[/tex]

Required

Time it hits the ground

When the object hits the ground, the height is 0.

In other words:

f(t) = 0

So, we have:

[tex]0= 100-4.9t^2[/tex]

Collect like terms

[tex]4.9t^2 = 100[/tex]

Divide through by 4.9

[tex]t^2 = \frac{100}{4.9}[/tex]

[tex]t^2 = 20.4081632653[/tex]

Take positive square roots of both sides

[tex]t = \sqrt{20.4081632653}[/tex]

[tex]t = 4.51753951453[/tex]

[tex]t = 4.52[/tex]

Hence, the ball hits the ground after 4.52 seconds

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