The equation \(y = -6t^2 + 43t\)describes the height (in feet) of a projectile t seconds after it is launched from the surface of Mars at 43 feet per second. In how many seconds will the projectile first reach 77 feet in height? Express your answer as a decimal rounded to the nearest tenth.
Some may say 77/43 seconds, however gravity takes an affect but is graphed by the equation y=-6t^2 + 43t.
Plugging in 77 = -6t^2 + 43t, you can use the quadratic formula on 6t^2 - 43t + 77 or factor to (3t - 11)(2t - 7) = 0.
From zero product property, we have t = 3.66666 and 3.5. We pick the smaller time because that is first when the projectile reaches 77 feet so the answer is 3.5 seconds.