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The equation y = -6t^2 + 43t describes the height (in feet) of a projectile  seconds after it is launched from the surface of Mars at 43 feet per second. In how many seconds will the projectile first reach $$27$$ feet in height? Express your answer as a decimal rounded to the nearest tenth.

Feb 7, 2022

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Plug 27 in to the quadratic: $$27 = -6t^2+43t$$

Subtract 27 from both sides to make it a quadratic: $$0 = -6t^2+43t-27$$

Plug it in to the quadratic formula: $$t ={-43 \pm \sqrt{43^2-4\times -6 \times -27} \over 2\times -6}$$

There are 2 solutions, one at $$t\approx6.5$$ seconds, and the other at $$t\approx0.7$$ seconds.

We want the smaller answer, so  $$\color{brown}\boxed {t \approx 0.7}$$

Feb 7, 2022