It will reach 80 feet for the second time after 5 seconds.

We set the equation equal to 80 feet:

80= -16t² + 96t

When solving quadratics, we want it equal to 0, so we subtract 80 from both sides:

80-80= -16t² + 96t - 80

0= -16t² + 96t - 80

We use the quadratic formula to solve:

We set the equation equal to 80 feet:

80= -16t² + 96t

When solving quadratics, we want it equal to 0, so we subtract 80 from both sides:

80-80= -16t² + 96t - 80

0= -16t² + 96t - 80

We use the quadratic formula to solve:

To solve the problem, substitute 80 feet to value of h(t). so given that

h(t) = -16t^2 + 96t

so

h(t) = -16t^2 + 96t = 80

-16t^2 + 96t - 80 = 0

divide the whole equation with -16

( -16t^2 + 96t - 80 = 0) 1/-16

t^2 - 6t + 5 = 0

factor the quadratic equation

( t - 5 ) ( t - 1 ) = 0

t = 5

t = 1

so the answer would be 5 s, because it the rocket will reach the 80 ft for the first time at 1 s

h(t) = -16t^2 + 96t

so

h(t) = -16t^2 + 96t = 80

-16t^2 + 96t - 80 = 0

divide the whole equation with -16

( -16t^2 + 96t - 80 = 0) 1/-16

t^2 - 6t + 5 = 0

factor the quadratic equation

( t - 5 ) ( t - 1 ) = 0

t = 5

t = 1

so the answer would be 5 s, because it the rocket will reach the 80 ft for the first time at 1 s

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