Question

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?

Answer 1

`h=-16t^(2)+64t+80`

We set
`h=0`:

`-16t^(2)+64t+80=0`

`\Rightarrow t^(2)-4t-5=0`

`\Rightarrow (t+1)(t-5)=0`

`\Rightarrow t=-1` or
`t=5`
We use
`t=5` because a negative number wouldn't make sense

So the object hits the ground after 5 seconds.

Answer 2

Answer:The object will hit the ground after 5 seconds

Explanation:

Given height of tower =80 ft

h=-16
`t^(2)`+64t+80

When the object will hit the ground its height=0

0=-16
`t^(2)`+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