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

Answer:The object will hit the ground after 5 seconds

Step-by-step 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

Answer 2

$h=-16t^{2}+64t+80$

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.