help me pleaseeee

Question

A flare is launched from the deck of a lifeboat 8 ft above the water surface. The initial upward velocity is 120 feet per second.

(Vertical Motion Model: h(t) = -16t2 + vt + s)

How many seconds will it take for the flare to return to the sea?

Answer 1

With the initial conditions given,

h(t) =-16t²+120t + 8

Sea level is zero, so need to solve

-16t²+120t+8 = 0 --> -2t²+15t+1 = 0

Using the quadratic equation t = -.13, 15.32. Take the positive value, t = 15.32 seconds

Answer 2

At t=0 h(t) = 8, so s = 8

v = 120

h(t) = -16t² + 120t + 8

So you need to find t when h(t) = -8

-8 = -16t² + 120t + 8

16t² - 120t - 16 = 0

You could plot y = 16x² - 120x - 16 on Desmos and then read off the x value when y=0

or factorise the quadratic