Quadratic world problem

Question

A diver jumps off a diving board that is 6 ft above the water at a velocity of 12 ft/sec. His height, s , in feet, above the water can be modeled by s(t)=-16t^2+12t+6.

(a) How long is the diver in the air before he hits the water? 

Enter the exact answer. 

The diver is in the air for ____ seconds. 

(b) What is the maximum height achieved and when does it occur? 

Enter the exact answers. 

The maximum height is ____ feet, and it occurs after ____seconds.

Answer 1

(a) -16t^2 + 12t + 6 = 0

-8t^2 + 6t + 3 = 0

8t^2 - 6t - 3 = 0

[6 +or- sqrt( 36 - 4*8* -3)] / 16

[ 6 +or- sqrt(132)]/16

[6 +or- sqrt(2*66)]/16

[6 +or- sqrt(2*2*33)]/16

[6 +or- 2 * sqrt(33)]/16

[3 +or- sqrt(33)]/8

negative branch is disqualified because it results in negative measures

[3 + sqrt(33)]/ 8 = 1.0930703308172535824813264335274.....

The diver is in the air for 1.0930703308172535824813264335274..... seconds.

(b) -b/(2a) = (-12)/(2*-16) = -12/-32 = 6/16 = 3/8

-16(3/8)^2 + 12(3/8) + 6 = -16 ( 9/64) + 36/8 + 6 = -9/4 + 36/8 + 6 = -18/8 + 36/8 + 6 =

18/8 + 6 = 9/4 + 6 = 9/4 + 24/4 = 33/4

The max height is 33/4 feet and occurs after 3/8 seconds