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An object is thrown upward from the top of 80 ft tower.The height h of the object after t seconds is represented by the quadratic equation h=-16t^2+64t+80.After how many seconds will the object hit the ground?

Respuesta :

bartdrinksmalk
[tex]h=-16t^{2}+64t+80[/tex]

We set [tex]h=0[/tex]:
[tex]-16t^{2}+64t+80=0[/tex]
[tex]\Rightarrow t^{2}-4t-5=0[/tex]
[tex]\Rightarrow (t+1)(t-5)=0[/tex]
[tex]\Rightarrow t=-1[/tex] or [tex]t=5[/tex]
We use [tex]t=5[/tex] because a negative number wouldn't make sense

So the object hits the ground after 5 seconds.

Answer:The object will hit the ground after 5 seconds


Step-by-step explanation:

Given height of tower =80 ft

h=-16[tex]t^{2}[/tex]+64t+80

When the object will hit the ground its height=0

0=-16[tex]t^{2}[/tex]+64t+80

Multiplying both sides by -1

16t²-64t-80=0

Dividing by 16 both sides

t²-4t-5=0

(t-5)(t+1)=0

t=5 or -1

So t=5 since time cannot be negative

The object will fall after 5 seconds



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