word problem challenge!!!?

Question

Word problem challenge...?
This has two parts... I am stumped!!!

A runner reached a speed of 32 ft/sec on the pole vault runway, his height above the groud t seconds after leaving the ground was given by h = -16t^2 + 32t. (the elasticity of the pole converts the horizontal speed into vertical speed.) Find the value of t for which is height was 12 ft.

THEN...

use this information to determine how long Johnson was int he air. For how long was he more than 14 ft in the air??

OMG!!! Pulling hair out!

Answer 1

The key here is use the quadratic formula.

h = -16t^2 + 32t
12 = -16t^2 + 32t
0 = -16t^2 + 32t - 12
0 = 16t^2 - 32t + 12

t = (-b +/- √(b^2 - 4ac)) / 2a
t = (32 +/- √(32^2 - 4(16)(12))) / 32
t = 1 +/- √(256) / 32
t = 1 +/- 16/32
t = .5 sec, 1.5 sec

Use the same method to answer the rest of the problem, but substitute other values of h (0 and 14) and solve again.

Answer 2

Presuming you mean g, as in weight = mg for the "fee of gravity, why might I do all that pulley and harmonics stuff? Why no longer in basic terms use S = a million/2 gt^2; so as that g = sqrt(2S)/t. the place S is your huge-unfold peak (you had to bypass a actual to pass on the area flight; so which you will possibly comprehend how tall you have been), t = the time to drop any merchandise (at the same time with that a million.22 kg weight in case you prefer) from S, as measured by ability of your very precise Rolex. i might do this test approximately 30 circumstances or so, calculate the priority-loose g and huge-unfold deviation for the inhabitants of documents, and positioned up that back to headquarters.