A stone is thrown upward from the top of a building.

Question

A stone is thrown upward from the top of a building. Its height (in feet) above the ground after t seconds is given by the function ℎ(𝑡) = −16𝑡 2 + 96𝑡 + 48. How long does it take the stone to hit the ground? Give an exact value.

Answer 1

0 = -16 t^2 + 96t + 48

0 = t^2 -6t - 3

t = [6 +or- sqrt ( 36 + 12)] / 2

= [6 +or- sqrt(48)]/ 2

= [6 +or- 4*sqrt(3)] / 2

negative branch leads to negative measures

t = [6 + 4 * sqrt(3)] / 2