You have to ask yourself the meaning of h(0) That means that GS Hopper is at this starting position h(0) = -0^2 + 4/3 * 0 + 1/4 GS is 1/4 of a unit above the ground. So you need to find out how to solve h(t) so that the value of h(t) = 0 There is a difference between h(t) = 0 and t = 0.
-t^2 + 4/3 t + 1/4 = 0 I'd multiply through be 12. It might be easier to do. -12 t^2 + 16t + 3 = 0 Remember all terms have to be multiplied by 12. I know this seems laborious, but you should divide through by - 1 12t^1 - 16t - 3 = 0. That way you don't have to explain what to do with the minus 1. Negatives can be a real pain.
It does factor. (2x - 3)(6x + 1) = 0 This is just a guess that was lucky. You have to try combinations to get it right. Luckily 3 has only 1 and 3 as factors. 2x - 3 = 0 2x = 3 x = 3/2 x = 1.5 This answer means that 1.5 s starts his jump, he's on the ground.
the other root is meaningless. You can't have minus time in these questions. Answer t = 1.5 s <<<< answer
