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The equation y = -6t^2 + 51t describes the height (in feet) of a projectile launched from the surface of Mars at 51 feet per second. In how many seconds will the projectile first reach 120 feet in height?

Oct 4, 2021

#1
+13577
+2

In how many seconds will the projectile first reach 120 feet in height?

Hello Guest!

$$f(t)=-6t^2+51t\\ \frac{df(t)}{dt}=-12t+51=0\\ t=4.25$$

$$h_{max}=-6\cdot 4.25^2+51\cdot 4.25$$

$$h_{max}=\color{blue}108.375\ feet$$

The projectile cannot reach a height of 120 feet.

!

Oct 4, 2021
#2
+36416
+1

120 = -6t^2 + 51 t

-6t^2 + 51 t -120 = 0    Quadratic formula show t = imaginary numbers ..... no answer ...as asinus found !

Oct 4, 2021