if an object is dropped from a height of 85 feet the function h(t)=-16^2+85 gives the height of the object after t second . Approximately how long will it take for the object to hit the ground?

Question

ybarrap · Answer

Solve for h(t)=85 for t.

Does this make sense?

anonymous · Answer

i have no idea how to do these

ybarrap · Answer

Is the equation
$$
h(t)=-16t^2+85
$$
?

anonymous · Answer

yes

ybarrap · Answer

Let's solve h(t) for t:
$$
h(t)=-16t^2+85\
-16t^2=h(t)-85\
16t^2=-h(t)+85\
t^2=\cfrac{-h(t)+85}{16}\
t=\sqrt{\cfrac{-h(t)+85}{16}}
$$
Do you know what to do from here?

ybarrap · Answer

?

ipwnbunnies · Answer

I think it'd be easier to go back to ybarrap"s first suggestion. Set h(t) = 0, then solve for t. When h(t) = 0, that means the object is at ground level. The problem becomes a simple two-step algebra problem.

ipwnbunnies · Answer

$$h(t) = 0 = -16t^{2} + 85$$