Question

An arrow is shot upward with a velocity of 64 feet per second. Using the formula h(t)=64t-16t^2, how long after the arrow is released does it hit the ground?

Answer 1

It hits the ground when h(t)=0

-16t^2+64t=0 factor

-16t(t-4)=0, we know t>0 so

t=4 seconds.

Answer 2

After the 4 second arrow is released, it will hit the ground.

Explanation:

Consider the provided formula.

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

We need to find how long after the arrow is released does it hit the ground.

If the arrow hit the ground that means the value of h(t)=0.

Substitute the value of h(t)=0 and solve the equation as shown.

`64t-16t^2=0`

`16t(4-t)=0`

Now use zero product rule: If ab=0 then either a=0 or b=0

`16t=0\ or\ 4-t=0`

`t=0\ or\ -t=-4`

`t=0\ or\ t=4`

Hence, after the 4 second arrow is released, it will hit the ground.