I have no idea how to do this... Help?

Question

A baking soda rocket is fired upwards with a initial speed of 80 feet per second. Its height,h, above the ground in feet can be modeled using the equation:

h(t)=-16t^2+80t where t is the time since launch in seconds

At what time, t>0, does the rocket hit the ground? Find algebraically using factoring.

Help me please!!!!

Answer 1

The equation h(t)=-16t²+80t gives you the height in feet, and "t" represents time in seconds.

When the rocket hits the ground the height is zero. Replace the height in the equation with zero ⇒ h(t) = 0, and then factore, use zero-factor property and solve for time "t"

See below what I mean:

h(t)=-16t²+80t

0 = -16t²+80t

0 = -16t (t-5)

0= -16t and 0= (t-5)

0=t 5=t ⇒ use time greater than zero t>0

so the rocket hits the ground at 5 seconds

Answer 2

When the rocket hits the ground, h = 0, right?

-16t² + 80t = 0

-16t(t - 5) = 0

In order for the left side to equal 0, one of the factors has to equal 0.

-16t = 0

t = 0

Well, that would be the launch time.

t - 5 = 0

t = 5 seconds