h(𝑡) = −6𝑡2 + 18𝑡 + 48

Question

A Martian standing on top of a boulder has tossed a rock vertically upward. The quadratic function below models the height of the rock, h(𝑡), in feet, 𝑡 seconds after it was thrown.

h(𝑡) = −6𝑡2 + 18𝑡 + 48

How long will it take for the rock to hit the surface of Mars? (Round your answer to the nearest tenth.)

Answer 1

-6t^2+18t +48 = 0

t^2 - 3t -8 = 0

t= 3/2 +.5sqr(9+32)

t = 1.5 +.5sqr41

= about 4.7 seconds to hit Mars ground

h(4.7) = -6(4.7)^2 +18(4.7) +48

= .06 which is close to zero, given rounding errors

indicating time is actually slightly more than 4.7 seconds